Greek Koine was the dialect of Greek used in the Hellenistic empires formed after the death of Alexander the Great.
The Old Testament was written almost entirely in Hebrew, with a small amount written in Aramaic, a related Semitic language. It was translated into Greek Koine.
The Gospels of the New Testament were written in Greek Koine. Paul's epsitles were also written in Greek. The remaining books of the New Testament were all written in Greek Koine in the final form in which they have come down to us, but some may have earlier layers (sections) that were written in Hebrew or Aramaic.