There is no scholarly consensus as to when the Hebrew Bible canon was fixed: some scholars argue that it was fixed by the Hasmonean dynasty (140-40 BCE),[5] while others argue it was not fixed until the second century CE or even later.[6] The Catholic Pontifical Biblical Commission says that "the more restricted Hebrew canon is later than the formation of the New Testament".[7]
On the New Testament:
For the Orthodox, the recognition of these writings as authoritative was formalized in the Second Council of Trullan of 692, although it was nearly universally accepted in the mid 300s.[1] The Catholic Church made dogmatic definition upon its Biblical canon at the Council of Trent of 1546, reaffirmed the Canons of Florence of 1442 and North African Councils (Hippo and Carthage) of 393-419.[2][3] For the Church of England, it was made dogmatic on the Thirty-Nine Articles of 1563; for Calvinism, on the Westminster Confession of Faith of 1647.
So, the formalization of the basic outline goes back to 393. Back to Wikipedia:
Marcion of Sinope, a bishop of Asia Minor who went to Rome and was later excommunicated for his views, was the first of record to propose a definitive, exclusive, unique list of Christian scriptures, compiled sometime between 130–40 AD.[24]
An excellent read and source document is Pagans: The End of Traditional Religion and Rise of Christianity....which covers the Roman Empire and how various religions were forced out, and the Catholic Church spread across Europe.