The Septuagint translators and New Testament authors chose diatheke because in its original use, before the Greeks came to use it to mean "testament," it had reference to what is called "the disposition for ones self."
A diatheke had to do with an individuals disposition of his goods or property for himself; that is, it referred to his sovereign determining of his heirs. To this day, thats how we understand the concept of a testament or will.
That aspect of disposition is an element that reflects the Hebrew concept because in His covenant, God sovereignly determines to give promises to whom He will give promises. He made a covenant with Abraham, not Hammurabi. He chose the Jews, not the Philistines. He entered into a covenant relationship with them and said, ”I will be your God and you will be my people." Thats a choice God made, not the Jews. So, even though the Greek word diatheke includes aspects that dont overlap with the Hebrew notion of a covenant, it carries the key notion of sovereign determination.
~ DR. R. C. SPROUT