Domonic Whilby, 22, faces 10 charges including manslaughter and grand larceny, the New York Daily News reported Thursday.
The driver of the bus, William Pena, 49, died when he was thrown from the vehicle in the early-morning accident Wednesday in Greenwich Village.
Whilby was reportedly escorted from a birthday party at the club 1 Oak for model Shaik about two blocks from the crash about 3:30 a.m. He was then ejected from a hotel where he was found passed out.
The truck, a delivery van for 18 Rabbits Granola, was parked in a hotel garage near the site of the birthday party at the time it was stolen.
The crash sent both vehicles into the side of a building.
Whilby was treated for minor neck injuries, police said, and was arrested at the scene.
The passengers on the bus, and a person on a scooter dragged by the truck, received non-life-threatening injuries.
Beckford's publicist said he was unaware of the incident, but relatives confirmed the family connection.
Celebrity Couples of 2014 [PHOTOS]