The canon was settled by the Catholic Church in the late 300s. Jerome, who was involved in translating the Bible into Latin during those times, dutifully noted, as any good researcher should, that some Jews of the day had a different OT canon. Today we call this a footnote, but Jerome received criticism for his words. In 402 A.D. Jerome responded to the critics to clarify:
What sin have I committed if I followed the judgment of the churches? But he who brings charges against me for relating the objections that the Hebrews are wont to raise against the Story of Susanna, the Song of the Three Children, and the story of Bel and the Dragon, which are not found in the Hebrew volume, proves that he is just a foolish sycophant. For I was not relating my own personal views, but rather the remarks that they [the Jews] are wont to make against us. (Against Rufinus, 11:33 [AD 402]).
Saint Athanasius is credited with the first Biblical canon (NT) containing the same books in the same order we use today. The list is contained in his Thirty-Ninth Festal Letter of 367 A.D. This list was approved by Pope Damasus, and formally approved of by Councils at Hippo and Carthage in the late 300s. Pope Innocent I wrote a letter to the Bishop of Toulouse in 405 A.D. containing the list. The list was re-affirmed at Carthage in 419 A.D., by the Council of Florence 1442 A.D., and by the Council of Trent in 1546 A.D.