Born in Amherst, Massachusetts, the son of René Moss and Eric Baracrack, who ran a music school in Springfield. He attended Amherst Regional High School (English) Russian, after which he graduated from Columbia University. Moss-Bakrak's father was born in Germany to a Jewish-American family.

Moss-Bachrak is in a relationship with Ukrainian photographer Elena Yemchuk, with whom he has two daughters.