They were actually a bunch of Turkic tribes originating from the Turkmen Plateau. They converted to Islam and later invaded Turkey and kicked the Christians out of there. They were always their own people. I think they descended from Genghis Khan or something?
There were two major phases of the conversion of the Turkic people.
One was during the conquest of central Asia in the 7th and 8th century and the second after the defeat of the Mongol hordes by the Muslims, their first defeat, in the 13th century.
That defeat came at the hands of fellow Turkic ppl who were rulers of Egypt at the time, The Mamluks.
The defeated Mongols became Muslims and later moved West into Anatolia and established The Ottoman Empire.
Genghis Khan and his descendants wiped away a lot of Muslims and in the process brought down the last Arab rule of Islamic world, The Abassids. Although it is said that the ruler or khalif at the time was just a puppet and the real rulers were The Seljuks, a muslim Turkic dynasty.
Out of the ashes of the Abassids rose The Ottomans who raised the banner of Islam. The first non Arab rulers of the Muslim world until their demise early in the 20th century at the hands of Western nations and their Arab puppets.