The word “testament” in the designations “Old Testament” and “New Testament,” given to the two divisions of the Bible, goes back through Latin testamentum to Greek diatheke, which in most of its occurrences in the Greek Bible means “covenant” rather than “testament.”
In Jeremiah 31:31, a new covenant is foretold that will supersede that which God made with Israel in the wilderness (cf. Exod. 24:7ff.). “By calling this covenant ‘new,’ he has made the first one obsolete” (Heb. 8:13, NIV). The New Testament writers see the fulfillment of the prophecy of the new covenant in the new order inaugurated by the work of Christ; his own words of institution (1 Cor. 11:25) give the authority for this interpretation.
The Old Testament books, then, are so called because of their close association with the history of the “old covenant”; the New Testament books are so called because they are the foundation documents of the “new covenant.” An approach to our common use of the term “Old Testament” appears in 2 Corinthians 3:14, “when the old covenant is read,” although Paul probably means the law, the basis of the old covenant, rather than the whole volume of Hebrew Scripture. The terms “Old Testament” and “New Testament” for the two collections of books came into general Christian use in the later part of the second century; Tertullian rendered diatheke into Latin by instrumentum (a legal document) and also by testamentum; it was the latter word that survived, unfortunately, since the two parts of the Bible are not “testaments” in the ordinary sense of the term.
This is an excerpt from The Origin of the Bible by F. F. Bruce, J. I. Packer, Philip Comfort, and Carl F. H. Henry. To read more, you can purchase this book from many Christian bookstores and online retailers, including Tyndale.com: https://www.tyndale.com/p/the-origin-of-the-bible/9781414379326
Bruce, F. F., et al. The Origin of the Bible. Carol Stream, IL: Tyndale House Publishers, 2020.