What is the Orthodox canon? What books does the Orthodox Bible contain? Additionally, when was this settled (if it is settled) and how was it decided?
The Orthodox canon of the Old Testament is close to the Septuagint both by the order of books and by the contents.
However, the Canonical books are those that were originally included in the Jewish canon, with several additions. 60th rule of the Council of Laodicea (about A.D. 363) names 22 books within the Old Testament. They were reorganized and split during the centuries to coincide more with the Septuagint.

The Russian Orthodox tradition includes 39 canonical (coinciding with the Protestant Old Testament) and 11 non-canonical books, thus having a distinction from Catholic Vulgata that contains 46 canonical books forming the Old Testament.

The 11 non-canonical books are: 7, that are known as Deuterocanonical in Catholic canon (Tobias, Judith, Wisdom, Sirach or Ecclesiasticus, Baruch, 1 Maccabees, 2 Maccabees), the Letter of Jeremiah as the separate book from Baruch, and the other 3: 1 Esdras, 3 Maccabees, 3 Esdras. 
These non-canonical books are considered as not written under the Holy Spirit, but are accepted by many Fathers.

From the thirty-ninth Letter of Holy Athanasius, Bishop of Alexandria, on the Paschal festival:


  
  There are, then, of the Old Testament, twenty-two books in number; for, as I have heard, it is handed down that this is the number of the letters among the Hebrews; their respective order and names being as follows. The first is Genesis, then Exodus, next Leviticus, after that Numbers, and then Deuteronomy. Following these there is Joshua, the son of Nun, then Judges, then Ruth. And again, after these four books of Kings, the first and second being reckoned as one book, and so likewise the third and fourth as one book. And again, the first and second of the Chronicles are reckoned as one book. Again Ezra, the first and second are similarly one book. After these there is the book of Psalms, then the Proverbs, next Ecclesiastes, and the Song of Songs. Job follows, then the Prophets, the twelve being reckoned as one book. Then Isaiah, one book, then Jeremiah with Baruch, Lamentations, and the epistle, one book; afterwards, Ezekiel and Daniel, each one book. Thus far constitutes the Old Testament.
  Again it is not tedious to speak of the [books] of the New Testament. These are, the four Gospels, according to Matthew, Mark, Luke, and John. Afterwards, the Acts of the Apostles and Epistles (called Catholic), seven, viz. of James, one; of Peter, two; of John, three; after these, one of Jude. In addition, there are fourteen Epistles of Paul, written in this order. The first, to the Romans; then two to the Corinthians; after these, to the Galatians; next, to the Ephesians; then to the Philippians; then to the Colossians; after these, two to the Thessalonians, and that to the Hebrews; and again, two to Timothy; one to Titus; and lastly, that to Philemon. And besides, the Revelation of John.
  These are fountains of salvation, that they who thirst may be satisfied with the living words they contain. In these alone is proclaimed the doctrine of godliness. Let no man add to these, neither let him take ought from these. For concerning these the Lord put to shame the Sadducees, and said, 'You err, not knowing the Scriptures.' And He reproved the Jews, saying, 'Search the Scriptures, for these are they that testify of Me Matthew 22:29; John 5:39.'
  But for greater exactness I add this also, writing of necessity; that there are other books besides these not indeed included in the Canon, but appointed by the Fathers to be read by those who newly join us, and who wish for instruction in the word of godliness. The Wisdom of Solomon, and the Wisdom of Sirach, and Esther, and Judith, and Tobit, and that which is called the Teaching of the Apostles, and the Shepherd.
  


The Orthodox Synod, convened in Constantinople in 1642, made a decision that is similar to the aforementioned words of Athanasius of Alexandria: the argued books of Old Testament "are non-canonical", but "are venerated as beneficent and pious" (ref. in Russian).

The Prayer of Manasseh is agreed to be non-canonical by all Christian denominations, but it is placed in different parts of the Bible by different Churches. In the Russian Orthodox tradition (also in the late 4th-century Vulgate and the Ethiopian Bible) it is placed at the end of 2 Chronicles, after 36:23 (ref. in Russian).

The list of non-canonical books accepted by the Greek Orthodox Church differs a bit from the list of the Russian Orthodox Church. It contains 4 Maccabees, but does not include 3 Esdras.

27 books of the New Testament are the same for the most of Cristian denominations. The full list on Wikipedia is correct.