The development of Biblical canon is a complex topic. Indeed most of the OT probably existed in ancient times as Jewish meditation literature, and religious/historical writings. And all of what we know as the old Testament is likely to have existed before the time of Christ.

However, the process of canonization was a slow one, in 90 and 118 AD the books known as the old testament are established as Authoritative by the Councils of Jamnia.

The New Testament was probably written in the first or second century AD and took some time to be accepted. The short version is that the Council of Carthage in 397 AD established the 27 books of the New testament as canon and Jerome translated the 66 books of the Bible into Latin as the Vulgate bible in 400AD.

However the long version is interesting and well worth studying. Marcion's heretical NT, the Persecution of Diocletian, Athanasius' festal letter, Saint Augustine and and the Council of Carthage are all very interesting, worth going into (alas that I have not the time with my work,)

The issue with deuterocannonical books (apocrypha) is still in a sense widely debated. Martin Luther excluded these from the Bible but catholic and Orthodox tradition including them. The Council of Trent in 1545-63 confirmed Catholic canon to mean the 66 books of the bible along with 7 Apocryphal books and additions to the books of Daniel and Esther.

Hope this helps.