Some quick background to the answer:
The most fundamental belief in Islam is that we believe there is only one God (Allah, in Arabic), and so one who submits to the word of Allah is a Muslim. We also believe that there were thousands of prophets who came over the course of history to preach the word of God, like Noah, Abraham, Jesus, Moses, David, etc. (peace be upon them all). The final messenger was Muhammad (peace and blessings be upon him).
Muslims also believe that all these prophets preached the same message since the beginning of time: there is only one God worthy of worship, so worship Him. Sometimes, this message became corrupted or lost, so another messenger would come, until the very last one came. We believe all of these prophets to be Muslim, in the sense that they believed in one God, worshipped Him, and taught the exact same message. However, obviously we don't call them "Muslim," but we would call them Jewish or Christian, etc. So Islam is just a continuation of that same message, if you will. Therefore, we consider this message to be as old as the human race, since Adam (peace be upon him) was also a Muslim (one who submits to the word of God).