The Islamic calendar begins from the Prophet's (peace and blessings be upon him) Hijrah to Madinah

It is narrated from Sayyiduna Sahl bin Sa'd (may Allah be pleased with him) that he said: "The people erred in the count (of the Hijri calendar): they did not reckon from the year of his (peace and blessings be upon him) prophetic mission, nor from the year of his (peace and blessings be upon him) death; rather, they reckoned the dates only from the time of his (peace and blessings be upon him) arrival in Madinah al-Munawwarah."
This hadith is sahih (authentic) on the condition of the two Shaykhs (Bukhari and Muslim), but they did not record it.

It is narrated from Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) that he said: "The (Hijri) calendar began from the year in which the Messenger of Allah (peace and blessings be upon him) arrived in Madinah, and in that same year Sayyiduna Abdullah bin al-Zubayr (may Allah be pleased with him) was born."
This hadith is sahih (authentic) on the condition of Muslim, but the two Shaykhs (Bukhari and Muslim) did not record it.