Strictly speaking, the term Jew applies to the descendants of the Israelite tribe of Judah. Judah was the fourth child born to Leah and Jacob (whose name was later changed to Israel). His name, whose name means "praise" in Hebrew (Genesis 29:35), is first person that can be considered a true Jew.
It should be noted that although Abraham was a Hebrew (Genesis 14:13) and circumcised (Romans 4:9 - 12) he is not, from a strict Biblical standpoint, a Jew. Additionally, Abraham's eight sons (Ishmael, Isaac, etc.), and his grandsons Jacob and Esau, are not Jews.
Judah, the first Jew, is a descendent of Abraham and Sarah through Isaac (Abraham's first and only son through Sarah). God considered Isaac the firstborn as far as receiving the birthright blessings (Genesis 17:19, 21:12, 25:5). Isaac's sons were Esau and Jacob (Genesis 25:24 - 28). Jacob (Israel) produced thirteen children, twelve of which were males. These sons became the twelve tribes of Israel, only one of which was (initially) considered to produce a Jew.
The designation of who was considered a Jew changed after the death of King Solomon. After his demise, the Kingdom of Israel split into two major pieces. The first, and biggest, piece was the northern kingdom of Israel with its capital at Samaria. It was composed of ten Israelite tribes. The second piece, the Kingdom of Judah, which continued to be ruled by Solomon's descendants, had its capital at Jerusalem. It ruled over the remaining tribes.
The three tribes Solomon's son Rehoboam, and his descendants, ruled over were Judah, Benjamin and Levi. The tribe of Benjamin stayed loyal to King David's sons, in part, because their inheritance in the land included Jerusalem. Most of the descendants of Levi, who were scattered throughout all the tribes, moved to the Kingdom of Judah in order to avoid worshipping the newly created false gods established at Samaria. Soon after Benjamin and Levi aligned themselves with Judah, people physically descended from all three tribes were called and considered a Jew.
The Old Testament defined a Jew based on physical lineage. In the New Testament, however, such lineages do not matter concerning God's blessings and salvation. The Apostle Paul taught that although a Gentile (non-Israelites) was not a Jew by birth, he became one spiritually by faith and therefore were consider by God to be His children.
For he is not a Jew who is one outwardly, neither is that circumcision which is external in the flesh; Rather, he is a Jew who is one inwardly, and circumcision is of the heart, in the spirit and not in the letter; whose praise is not from men but from God (Romans 2:28 - 29, HBFV).