This is a subsidiary post of Editorial Activity of the New Testament.
The order of the books in the New Testament was determined to some degree when the books first began circulating in subsets of what would become the New Testament: that is, collections such as the Gospels or the Letters of Paul.
There is an “Eastern” order (arrangement) of the books in the NT versus “Western” order of the books. This is a reference, respectively, to churches in the eastern part of the Roman Empire (e.g. Alexandria, Antioch, and Caesaria) vis-a-vis those in the western part (e.g. Rome, Carthage, Gaul).
The “Western order” of the Gospels is Matthew, John, Luke and Mark” (from Wikipedia article on Codex Bezae).
There are two ways order can vary: 1) the order of the sub-collections (e.g. whether the Pauline epistles precede or follow the General Epistles), and 2) the order of writings within a sub-collection (e.g. whether Hebrews follows Romans, 2 Thessalonians, or Philemon).
Compare the order of the the books in the lists we have from Athanasius, Jerome, Augustine and others.
Details about these sources can be found in Annotated Bibliography on New Testament Text and Canon.
Allert, 2007, p. 141 (He references scholar F. F. Bruce.)
Davidson, Samuel. The Canon of the Bible: Its Formation, History, and Fluctuations, Third Revised and Enlarged Edition. C. Kegan Paul & Co., 1877. “Chapter VIII – Order of the New Testament Books” p. 221-230.
Farmer, William R. “A Study of the Development of the New Testament Canon” in The Formation of the New Testament Canon: An Ecumenical Approach by Farmer and Farkasfalvy. Paulist Press, 1983. See p. 10, including especially footnote 3. See also p. 14.
Kelly, Joseph F. Why is there a New Testament? Michael Glazier, 1986. On p. 101 he briefly makes the important point that though Athanasius in 367 is the first extant list of New Testament books identical to the one we have, the order of books is not identical.
Kostenberger et al, 2009, Kindle location 884-943 “The Current Order of New Testament Books
Metzger, 1987, Appendix II, p. 295 “Variations in the Sequence of the Books of the New Testament”
Outler, Albert C. “The ‘Logic’ of Canon-making and the Tasks of Canon-criticism” (14 pages) in Texts and Testaments by March (bibliography). See especially p. 266-268.
Patzia, 2011, p. 176-183
Trobisch, 2000, p. 25
Trobisch, 2012, p. 897-901.