Johnson’s father’s father was a Turkish citizen. This Turkish grandfather however was half Circassian (his maternal line was from the Caucuses region of Russia), so really Boris is only 1/8 Turkish. He does undeniably have Muslim ancestors though. He also is the decendant of an American Jew (as well as English, Swiss, and French ancestors), making an unusual mixture. The UK TV show Who Do You Think You Are? once devoted an entire episode to unraveling Johnsons ancestry.
And he was born in New York despite his embarrassingly plummy accent.