Actually, the Persians and the peoples of the Maghreb were the first to be converted to Islam by the Arabs but if you are asking why most Turkic peoples today are Muslim then it has to do with several factors. First is location; the Turks originally inhabited (and still inhabit today) Central Asia in what is today Kazakhstan, Uzbekistan, Tajikistan, etc. which bordered the Muslim Abbasid Caliphate. Now the Turkic peoples, like most Central Asian steppe people, had a very pluralistic society. There were Turks of every religious stripe, including Jews and Nestorian Christians, alongside the native Central Asian shamanistic pagan faith, today referred to as Tengriism after the chief sky god Tengri. This tolerant policy made the Turks amenable to conversion so when the Oghuz, later called the Seljuk, Turks invaded and conqured the Abbasid Caliphate they quickly Islamized and Persianized. Those same Seljuk Turks would later go on to invade Asia Minor and form the Sultanate of Rum, the forerunner of the Ottoman Empire.