Yost graduated from the University of Michigan in 1995 with a film and video degree and got into advertising in the Detroit area, producing TV commercials.

He went on to earn an MFA in film from The Peter Stark Producing Program at the University of Southern California and later interned, in 2002, in Marvel Comics' west coast office.

His spec film scripts got attention from Marvel executives who hired Yost to write episodes of the TV series X-Men: Evolution.

On June 6, 2017, it was announced that Yost would write an American live-action adaptation of Cowboy Bebop for television with Tomorrow Studios, a partnership between Marty Adelstein and Sunrise Inc., which also produced the original anime.

In August 2024, Yost and Alan Wan served as showrunners and executive producers on Tales of the Teenage Mutant Ninja Turtles for Paramount+.