Greek culture was introduced throughout the world of the New Testament by Alexander the Great during the intertestamental period. A young military genius, Alexander conquered the entire Persian Empire and more through a series of brilliant campaigns (334-323 b.c.) Asia Minor came under his dominion in 334-333 b.c., Syro-Palestine in 332 b.c., and Egypt in 332-331 b.c. Alexander's vision included not only the conquest of the world but the propagation of Greek culture, i.e., the hellenization of all peoples.
Upon his death at the age of thirty-two, his kingdom was divided among three of his generals. Initially, Palestine fell under the rule of the Ptolemies of Egypt (323-198 b.c.); subsequently, the Seleucids of Antioch got the upper hand in the region and ruled briefly (198-164 b.c.). The important point here is that the population of the area was subject to direct Greek rule for more than 150 years.
During that time, the Greek language was imposed on the Jewish nation and became, furthermore, the lingua franca of the entire NT world. Thus, the NT was written in Greek, though Jesus, Paul, James, Peter, and John all doubtless spoke Aramaic and read Hebrew as well.
Another significant event, reflecting the influence of Greek culture on the Jews, was the translation of the OT from Hebrew into Greek. The dating of this translation, known as the Septuagint and designated LXX, is uncertain; it may have been done over an extended period (350-200 b.c.). The LXX became popular among the Jews dispersed throughout Egypt, Asia Minor, and even Palestine. The mother tongue of the Jews in those places was Greek. Moreover, the LXX is the Bible version that the NT authors quoted most often.
Finally, it is to be noted that the introduction of Greek culture gave rise to diverse and often conflicting responses on the part of the Jews. Moreover, the degree of assimilation by this alien culture varied widely in different regions (e.g., in Alexandria versus Jerusalem). Thus, this period is fraught with considerable tension and strife within the Jewish community, as some strove to preserve their biblical culture against the powerful influence of the Greek culture.