God Himself chose Moses to author the Pentateuch

"Then the LORD said to Moses, "Write this in a book as a memorial and recite it to Joshua, that I will utterly blot out the memory of Amalek from under heaven." (Ex 17:14)

"Then the LORD said to Moses, 'Write down these words, for in accordance with these words I have made a covenant with you and with Israel.' So he was there with the LORD forty days and forty nights; he did not eat bread or drink water. And he wrote on the tablets the words of the covenant, the Ten Commandments." (Ex 34:27-28)

"Only be strong and very courageous; be careful to do according to all the law which Moses My servant commanded you; do not turn from it to the right or to the left, so that you may have success wherever you go. This book of the law shall not depart from your mouth, but you shall meditate on it day and night, so that you may be careful to do according to all that is written in it; for then you will make your way prosperous, and then you will have success." (Josh 1:7-8)

The Pentateuch itself attests to Mosaic authorship

"Moses wrote down all the words of the LORD. Then he arose early in the morning, and built an altar at the foot of the mountain with twelve pillars for the twelve tribes of Israel." (Ex 24:4)

"These are the journeys of the sons of Israel, by which they came out from the land of Egypt by their armies, under the leadership of Moses and Aaron. Moses recorded their starting places according to their journeys by the command of the LORD, and these are their journeys according to their starting places." (Num 33:1-2)

"So Moses wrote this law and gave it to the priests, the sons of Levi who carried the ark of the covenant of the LORD, and to all the elders of Israel. Then Moses commanded them, saying, 'At the end of every seven years, at the time of the year of remission of debts, at the Feast of Booths, when all Israel comes to appear before the LORD your God at the place which He will choose, you shall read this law in front of all Israel in their hearing. Assemble the people, the men and the women and children and the alien who is in your town, so that they may hear and learn and fear the LORD your God, and be careful to observe all the words of this law. Their children, who have not known, will hear and learn to fear the LORD your God, as long as you live on the land which you are about to cross the Jordan to possess.'" (Deut 31:9-13)

"It came about, when Moses finished writing the words of this law in a book until they were complete, that Moses commanded the Levites who carried the ark of the covenant of the LORD, saying, 'Take this book of the law and place it beside the ark of the covenant of the LORD your God, that it may remain there as a witness against you.'"(Deut 31:24-26)

Joshua, the successor to Moses, recognized Mosaic authorship

"Then Joshua built an altar to the LORD, the God of Israel, in Mount Ebal, just as Moses the servant of the LORD had commanded the sons of Israel, as it is written in the book of the law of Moses, an altar of uncut stones on which no man had wielded an iron tool; and they offered burnt offerings on it to the LORD, and sacrificed peace offerings. He wrote there on the stones a copy of the law of Moses, which he had written, in the presence of the sons of Israel." (Josh 8:30-32)

"Be very firm, then, to keep and do all that is written in the book of the law of Moses, so that you may not turn aside from it to the right hand or to the left," (Josh 23:6)

King David acknowledged Mosaic authorship

"Keep the charge of the LORD your God, to walk in His ways, to keep His statutes, His commandments, His ordinances, and His testimonies, according to what is written in the Law of Moses, that you may succeed in all that you do and wherever you turn," (1 Kings 2:3)

The historian of Jewish kingships referred to Mosaic authorship

"But the sons of the slayers he did not put to death, according to what is written in the book of the Law of Moses, as the LORD commanded, saying, 'The fathers shall not be put to death for the sons, nor the sons be put to death for the fathers; but each shall be put to death for his own sin.'" (2 Kings 14:6)

"Then you will prosper, if you are careful to observe the statutes and the ordinances which the LORD commanded Moses concerning Israel. Be strong and courageous, do not fear nor be dismayed." (1 Chron 22:13)

"There was nothing in the ark except the two tablets which Moses put there at Horeb, where the LORD made a covenant with the sons of Israel, when they came out of Egypt." (2 Chron 5:10)

"Moreover, Jehoiada placed the offices of the house of the LORD under the authority of the Levitical priests, whom David had assigned over the house of the LORD, to offer the burnt offerings of the LORD, as it is written in the law of Moses--with rejoicing and singing according to the order of David." (2 Chron 23:18)

"However, he did not put their children to death, but did as it is written in the law in the book of Moses, which the LORD commanded, saying, 'Fathers shall not be put to death for sons, nor sons be put to death for fathers, but each shall be put to death for his own sin.'" (2 Chron 25:4)

"They stood at their stations after their custom, according to the law of Moses the man of God; the priests sprinkled the blood which they received from the hand of the Levites." (2 Chron 30:16)

"Then he put the carved image of the idol which he had made in the house of God, of which God had said to David and to Solomon his son, 'In this house and in Jerusalem, which I have chosen from all the tribes of Israel, I will put My name forever; and I will not again remove the foot of Israel from the land which I have appointed for your fathers, if only they will observe to do all that I have commanded them according to all the law, the statutes and the ordinances given through Moses.' Thus Manasseh misled Judah and the inhabitants of Jerusalem to do more evil than the nations whom the LORD destroyed before the sons of Israel." (2 Chron 33:7-9)

"When they were bringing out the money which had been brought into the house of the LORD, Hilkiah the priest found the book of the law of the LORD given by Moses." (2 Chron 34:14)

"Then they removed the burnt offerings that they might give them to the sections of the fathers' households of the lay people to present to the LORD, as it is written in the book of Moses. They did this also with the bulls." (2 Chron 35:12)

The prophets of God cited Mosaic authorship

"Then Jeshua the son of Jozadak and his brothers the priests, and Zerubbabel the son of Shealtiel and his brothers arose and built the altar of the God of Israel to offer burnt offerings on it, as it is written in the law of Moses, the man of God." (Ezra 3:2)

"Then they appointed the priests to their divisions and the Levites in their orders for the service of God in Jerusalem, as it is written in the book of Moses." (Ezra 6:18)

This Ezra went up from Babylon, and he was a scribe skilled in the law of Moses, which the LORD God of Israel had given; and the king granted him all he requested because the hand of the LORD his God was upon him." (Ezra 7:6)

"We have acted very corruptly against You and have not kept the commandments, nor the statutes, nor the ordinances which You commanded Your servant Moses. Remember the word which You commanded Your servant Moses, saying, 'If you are unfaithful I will scatter you among the peoples;'" (Neh 1:7-8)

"And all the people gathered as one man at the square which was in front of the Water Gate, and they asked Ezra the scribe to bring the book of the law of Moses which the LORD had given to Israel." (Neh 8:1)

"They found written in the law how the LORD had commanded through Moses that the sons of Israel should live in booths during the feast of the seventh month." (Neh 8:14)

"So You made known to them Your holy sabbath, and laid down for them commandments, statutes and law, through Your servant Moses." (Neh 9:14)

"are joining with their kinsmen, their nobles, and are taking on themselves a curse and an oath to walk in God's law, which was given through Moses, God's servant, and to keep and to observe all the commandments of GOD our Lord, and His ordinances and His statutes;" (Neh 10:29)

"On that day they read aloud from the book of Moses in the hearing of the people; and there was found written in it that no Ammonite or Moabite should ever enter the assembly of God," (Neh 13:1)

"Indeed all Israel has transgressed Your law and turned aside, not obeying Your voice; so the curse has been poured out on us, along with the oath which is written in the law of Moses the servant of God, for we have sinned against Him." (Dan 9:11)

"As it is written in the law of Moses, all this calamity has come on us; yet we have not sought the favor of the LORD our God by turning from our iniquity and giving attention to Your truth." (Dan 9:13)

"Remember the law of Moses My servant, even the statutes and ordinances which I commanded him in Horeb for all Israel." (Mal 4:4)

Jesus did not question Mosaic authorship

"And Jesus said to him, 'See that you tell no one; but go, show yourself to the priest and present the offering that Moses commanded, as a testimony to them.'" (Matt 8:4)

"They said to Him, 'Why then did Moses command to GIVE HER A CERTIFICATE OF DIVORCE AND SEND her AWAY?" He said to them, 'Because of your hardness of heart Moses permitted you to divorce your wives; but from the beginning it has not been this way.'" (Matt 19:7-8)

"and He said to him, 'See that you say nothing to anyone; but go, show yourself to the priest and offer for your cleansing what Moses commanded, as a testimony to them.'" (Mark 1:44)

"But regarding the fact that the dead rise again, have you not read in the book of Moses, in the passage about the burning bush, how God spoke to him, saying, 'I AM THE GOD OF ABRAHAM, AND THE GOD OF ISAAC, and the God of Jacob'?" (Mark 12:26)

"Then beginning with Moses and with all the prophets, He explained to them the things concerning Himself in all the Scriptures." (Luke 24:27)

"Now He said to them, 'These are My words which I spoke to you while I was still with you, that all things which are written about Me in the Law of Moses and the Prophets and the Psalms must be fulfilled.' Then He opened their minds to understand the Scriptures, and He said to them, 'Thus it is written, that the Christ would suffer and rise again from the dead the third day,'" (Luke 24:44-46)

"Do not think that I will accuse you before the Father; the one who accuses you is Moses, in whom you have set your hope. For if you believed Moses, you would believe Me, for he wrote about Me. But if you do not believe his writings, how will you believe My words?" (John 5:45-47)

"Did not Moses give you the Law, and yet none of you carries out the Law? Why do you seek to kill Me?" (John 7:19)

"If a man receives circumcision on the Sabbath so that the Law of Moses will not be broken, are you angry with Me because I made an entire man well on the Sabbath?" (John 7:23)

The Apostles referenced Mosaic authorship

"For the Law was given through Moses; grace and truth were realized through Jesus Christ." (John 1:17)

"Therefore let it be known to you, brethren, that through Him forgiveness of sins is proclaimed to you, and through Him everyone who believes is freed from all things, from which you could not be freed through the Law of Moses." (Acts 13:38-39)

"For Moses from ancient generations has in every city those who preach him, since he is read in the synagogues every Sabbath." (Acts 15:21)

"When they had set a day for Paul, they came to him at his lodging in large numbers; and he was explaining to them by solemnly testifying about the kingdom of God and trying to persuade them concerning Jesus, from both the Law of Moses and from the Prophets, from morning until evening." (Acts 28:23)

"For Moses writes that the man who practices the righteousness which is based on law shall live by that righteousness." (Rom 10:5)

"But I say, surely Israel did not know, did they? First Moses says, 'I WILL MAKE YOU JEALOUS BY THAT WHICH IS NOT A NATION, BY A NATION WITHOUT UNDERSTANDING WILL I ANGER YOU.'" (Rom 10:19)

"For it is written in the Law of Moses, 'YOU SHALL NOT MUZZLE THE OX WHILE HE IS THRESHING.' God is not concerned about oxen, is He?" (1 Cor 9:9)

"But their minds were hardened; for until this very day at the reading of the old covenant the same veil remains unlifted, because it is removed in Christ. But to this day whenever Moses is read, a veil lies over their heart; but whenever a person turns to the Lord, the veil is taken away." (2 Cor 3:14-16)

"For when every commandment had been spoken by Moses to all the people according to the Law, he took the blood of the calves and the goats, with water and scarlet wool and hyssop, and sprinkled both the book itself and all the people," (Heb 9:19)