Not completely. The books must be "Inspired". The books must have been written during the Apostolic Era. The books must have been written by an Apostle, or someone closely associated with an Apostle.
Also, Jesus defined the OT and the Apostle Peter recognized that Paul's writings were Scripture and Paul recognized Peter's writings as Scripture as well.
Luke 24:44 Then He said to them, "These are the words which I spoke to you while I was still with you, that all things must be fulfilled which were written in the Law of Moses and the Prophets and the Psalms concerning Me."
Paul quotes Luke's writings with Deuteronomy in ITim. 5:18 showing he considered them to be Scripture and Peter recognized Paul's writings as Scripture in 2Peter 3:15-16.
If you look at the few books that there was any debate about you find they do not affect the message of The Gospel in any way. For example the EO did not include Revelation until the ninth century and to this day do not read from it in services. The lack of controversy reveals how little question there was about what was "Inspired". It's also interesting to note that Jerome began his translation of the Vulgate before the Synod of Hippo. If there was a controversy surrounding which books were "Inspired" how would he have known which to include.