Islamic tradition holds that the Qur'an was dictated to Muhammad by Gabriel. This is the same Gabriel who was a messenger from God to the prophets of the Jewish Old Testament and who appeared to Elizabeth and Mary to announce their pregnancies with John the Baptist and Jesus, respectively.
It is important to remember that Islam recognizes the Torah and the Gospel of Jesus as being holy books sent by God through various prophets. All three monotheistic religions, Judaism, Christianity, and Islam, share a common basis of experiences, beginning with Abraham's acceptance of God's covenant. This common heritage indicates that Islam values scriptures from all these faiths, but does consider the Qur'an as the final and complete, authoritative expression of God's message to humanity.