How is it that Georgian Orthodox Church are in full communion with the Eastern Orthodox Church when they have a different biblical canon?

Guest37 above posts an excellent explanation of the gist of canon in Orthodoxy. I proffer a historically-rooted explanation of inclusion of additional books to the Canon of Scripture. The fact is that the Old Testament in Armenian usage contains the books in question. I found this out as a seminarian in New York. We went to the Armenian cathedral bookstore to purchase bibles, which they call “The Breath of God”, for this specific purpose to aid our seminary studies of scripture. The historical fact is that the Georgian and Armenian churches were in communion long after the Ecumenical Patriarchate broke communion with non-Chalcedonian ‘monophysite’ Churches. My educated guess is that the Georgians simply retained the old usage they must have shared with Armenians. Another example of Georgian outlier status is that the ‘Great Schism’ of 1054 did not obtain there and breaking communion with Rome was only instituted in Georgia later. This further exemplifies that fact that Orthodox Local Churches (autocephalies) do not necessarily follow practices laid out by the Phanar.

The 85th Apostolic Canon, ratified at the Quinisext Council in Trullo in 692, enumerated the list of Old Testament books:

Let the following books be counted venerable and sacred by all of you, both clergy and Laity. Of the Old Testament, five books of Moses, Genesis, Exodus, Leviticus, Numbers, Deuteronomy; of Joshua the Son of Nun, one; of the Judges, one; of Ruth, one; of the Kings, four; of the Chronicles of the book of the days, two; of Ezra, two; of Esther, one; [some texts read “of Judith, one”;] of the Maccabees, three; of Job, one; of the Psalter, one; of Solomon, three, viz.: Proverbs, Ecclesiastes, and the Song of Songs; of the Prophets, twelve; of Isaiah, one; of Jeremiah, one; of Ezekiel, one; of Daniel, one. But besides these you are recommended to teach your young persons the Wisdom of the very learned Sirach.

This Canon was adopted for the entire Church at the Seventh Ecumenical Council in Nicea in 787.

There is nothing in the Canon that prevents additional books from being included in the same binding, anymore that the Canon prohibits commentary or apparatus such as might appear in a study Bible.

An earlier local council, the Council of Carthage in 397, enumerated a similar list of books with the instruction that those listed were the only ones appointed to be read in the Church. The Church of Georgia follows the same Church Lectionary as the rest of the Eastern Orthodox Church, which does not include any of the books you indicate.

What's missing in the above answers I think is perhaps a couple of concepts that we Orthodox take for granted, but may not be readily apparent to Westerners.

First is the attitude towards Canon Law. In the West a law is a minimum, absolute standard. For example, if the speed limit is 55 and you drive 56, you're breaking the law. For the Orthodox the Canons are an expression of the shared experience of the whole Church. They record what the Church has already been doing, and what the whole Church has already accepted. That's why it takes a council of the whole Church together to create any canon. The fact that the Georgian Church has extra books in their canon, books that are ancient, were in common use, books that have been studied and vetted by the Church, containing nothing contrary to salvation, and books they don't use in their public liturgies, doesn't violate the requirement that the essential books be accepted. Lewis J. Patsavos, in his book 'Spiritual Dimensions of the Holy Canons,' writes, 'The canons are at the service of the Church; their function is to guide her members on the way to salvation and to make following that way easier.' [pp.4]

The second idea that is common to Orthodox is the Greek idea of oikonomia, which is usually translated 'economy,' although to us it means much more. It also encompasses the idea of generosity, allowance, philanthropy and loving care. The Church is called to look at the purpose of the Canon, not just the requirements of the text. The Church manages and ministers by the canons, having a vibrant, living relationship with them. She is not a slave to Canon Law, but instead she is called to evidence Christ's love through their application. Dr. Panteleimon Rodopoulos, Metropolitan of Tyroloë and Serention in his book 'An Overview of Orthodox Canon Law,' writes, 'In the implementation of Canon Law, particular importance is attached to the institution of economy, which makes it more flexible and subtle than any other branch of the law. Ecclesiastical economy is "the permitted temporary or permanent divergence from exactitude, either from need or for the sake of the greater benefit of certain members of of the Church as a whole, officially, under certain preconditions, and providing that respect remains unsullied and dogma intact." [pp 103] I'm sorry this was so long, but your question was important. I hope it helps.