There was an excellent article in this months This Rock magazine regarding the canon of scripture. I’ll try to summarize here and keep it simple.
During Jesus’ earthly ministry, there were 3 groups of Jews who used different versions of scripture. The Sadduccees considered only the Pentateuch (first 5 books) of Scripture to be inspired. The Pharisees used a canon containing the Pentateuch, Palms, Proverbs, and the Prophets as Scripture. The largest group of Jews did not live in Israel, however. They are called the diaspora (dispersed) Jews and used what was called the Alexandrian Canon, also known as the Septuagint.
Jesus is noted from quoting from all three versions, depending on whom He was addressing. When addressing Saduccees, He used Scripture from the Pentateuch. For the Pharisees, he used the “Law and the Prophets”, and with Greek Jews He used the Septuagint. St. Paul used the Septuagint almost exlusively, as most of his Jewish audience would be exclusively familiar with this version. As such, it was the canon of Scripture that was included in the Christian canon and affirmed at the Councils of Hippo, Carthage, and Rome, then formally at Trent.
There is an interesting historical event that many Protestants cite that they use to defend their use of an alternate canon, the Jewish Council of Jabneh (also called Jamnia or Gamnia). This council, called together after the Roman destruction of Jerusalem, was never an official doctrinal council. I.e., it did not have binding authority to declare a sealed canon. They got together to counter the “Christian heresy” and, because of Roman persecution, sought to exclude books from scripture that they consider had undue “Greek” influence.
Since the Pentacost began the Church Age, we no longer fall under the authority of the Sanhedron, but we fall under Apostolic Authority. Since the Apostles and their decendents have declared the books of the Septuagint to be the Canon of Scripture, that is the canon we follow. Here is an interesting link that provides more information.
kensmen.com/catholic/septuagint.html
Hope that helps. God Bless!!!