Thank you for the Biblical question, “When was the Bible divided into the Old and New Testament?”
Here are some thoughts for one’s consideration on the division of the Old Testament and New Testament:
A. By the time of the first century BCE, the Old Testament was recognized in a three fold section which for Jewish people it was known as the TaNaKh. That word stood as an acronym derived from the names of its three divisions: Torah (Instruction, or Law, also called the Pentateuch), Neviʾim (Prophets), and Ketuvim (Writings).
Jesus makes a reference to them in the Gospel of Luke:
Luke 24, “25 He said to them, “How foolish you are, and how slow to believe all that the prophets have spoken! 26 Did not the Messiah have to suffer these things and then enter his glory?” 27 And beginning with Moses and all the Prophets, he explained to them what was said in all the Scriptures concerning himself” (NIV).
Luke 24 also says this, “40 When he had said this, he showed them his hands and feet. 41 And while they still did not believe it because of joy and amazement, he asked them, “Do you have anything here to eat?” 42 They gave him a piece of broiled fish, 43 and he took it and ate it in their presence. 44 He said to them, “This is what I told you while I was still with you: Everything must be fulfilled that is written about me in the Law of Moses, the Prophets and the Psalms” (NIV).
The Jewish people refer to the scrolls as The Scriptures. Thus one can say The Scriptures of the Jewish People would be an appropriate designation.
B. By the end of the 2nd or 3rd century CE, the writings of the Apostles and their designees were mostly recognized by the early Church Fathers and the believers.
Luke 1 records that at the time of his writing that many writers have written about the words and works of Jesus. He says this, “Many have undertaken to draw up an account of the things that have been fulfilled[a] among us, 2 just as they were handed down to us by those who from the first were eyewitnesses and servants of the word. 3 With this in mind, since I myself have carefully investigated everything from the beginning, I too decided to write an orderly account for you, most excellent Theophilus, 4 so that you may know the certainty of the things you have been taught” (NIV),
Luke declares that many people have undertaken to record what has happened. Although there are no surviving written records of what other people wrote, the Gospels: Matthew, Mark, Luke, and John were widely received by the early Church. It would make sense that someone would have written what happen between the death of Christ and the spread of the Good News. The Acts of the Apostles was written to a follow letter to Theophilus, a personal letter, not addressed to the churches. As the Apostles responded to questions that the early church believers had, those letters were preserved and copied so that other churches can read them. Thus the writings were probably segmented to the life of Jesus which is called the Gospels of Jesus, and the letters to the churches or individuals.
Due to the persecution by the Jews and the teachings of Jesus by the Apostles with its clarification, there became a stark split between Jewish religious leaders and the Jewish people with the Apostles of Jesus and the followers of Jesus. It is more likely the followers of Jesus treasured/cherished more of the words of their Savior and Lord. They wanted to know more about Jesus.
With the ending of the religious persecution under the Roman Empire, Emperor Constantine declared/made “Christianity” the new religion of his empire. Constantine called a council of Christians leaders to Nicea, which became the Council of Nicea. It is at this Council that the Scriptures of the Jewish People, if I may use that designation, and the Words of the Jesus and the Apostles of the Christian believers were collected into one book. It is this Codex that combined both the Jewish Scriptures and the Words of Jesus and the Apostles.
The Codex Sinaiticus, dated to the 4th Century, is the oldest surviving Codex that has surviving “pages” of both the Old Testament Books and the New Testament Books. Were there other listings of New Testament? The Muratorian Canon, which is a partial listing, may reflect that the early church held to some listing of books that they believed were from the Apostles.
The designation of the Old Testament appears to come from Melito of Sardis in the 2nd century CE. Conversely, it would seem that the scrolls of the Gospels and the Letters would take on the designation of the New Testament. Thus the early Church Fathers recognized the Jewish Scriptures and the Words of Jesus and the Apostle.
SUMMARY: The Council of Nicea standardized the recognized books of the Jewish Scriptures and the words and works of Jesus and the Apostles in the fourth century CE.
For further discussion and perspectives:
https://www.quora.com/When-was-the-Bible-divided-into-the-Old-and-New-Testament