Rome’s canon was not definitively defined until Trent in the 1500s.
The canon of the Bible was defined by Pope Damasus I in the Council of Rome in 382 and by a series of councils in North Africa presided over by St. Augustine between 393 and 419. The same Pope Damasus also commissioned the Latin Vulgate edition of the Bible in 383 which contains the same list of books. From this point on this list of books for the Bible was accepted by the entire Western church. With a few exceptions, the Eastern church came to accept this same list of books in the 5th century. All that the Council of Trent did was restate what was already the accepted canon of Scripture.