This link has a more detailed version of when the books were chosen as part of the biblical canon.
http://staff.jccc.net/jbacon/readings/meetingjesus/BibleTimeline.htm
Here is part of the table of dates and events.
324 C.E.
Eusebius of Caesarea (Jerome)[20]
Translated Bible from Greek & Hebrew into Latin (Vulgate edition—early 5th Century)[21]
Early church historian lists in his Church History the following controversial books: Hebrews, Jude, 2 Peter, 2 and 3 John, and Revelation; plus other books no longer considered part of the canon such as The Shepherd, Acts of Paul, Apocalypse of Peter, Barnabas, and Teachings of the Apostles.
325 C.E.
Council of Nicea
Decisively ruled that that Jesus was both human and divine, and that he was equivalent to (literally, “of the same substance as”) God the Father. Resulted in making Arianism a heresy. The Nicene Creed encapsulated this theological doctrine.
350 C.E.
Cyril of Jerusalem
Lists acceptable books to read. Includes four gospels, “Acts of the twelve apostles; and in addition to these the seven catholic epistles of James, Peter, John, and Jude; and as a seal upon them all, and the latest work of disciples, the fourteen epistles of Paul. But let all the rest be put aside in a secondary rank.”
363 C.E.
Synod (Council) of Laodicea, first official church-wide body to define books in New Testament canon
Some say this list no longer exists, but Metzger lists them.[22]
367 C.E.
Athanasius, the bishop of Alexandria, compiled a list including all 27 books of the New Testament canon.
Athanasius, chief defender of the Nicene Creed. Known as “the Great”. 293?-373 C.E. The Greek patriarch of Alexandria and leading defender of Christian orthodoxy against Arianism.[23]
382 C.E.
Council of Rome
Produces list of Old and New Testament books (Galasian Decree) as know today. Prompted by Pope Damasus’ (366–384 C.E.) Decree. Same list as later adopted by the Council of Trent (1545–1563 C.E.).
393 C.E.
Council of Hippo[24]
Local North Africa Council of Bishops created the list of Old and New Testament books which forms the Roman Catholic Bible today.