Tomlin, 34, impressed the Steelers during the interview process with his organization skills, intelligence and grasp of the game, according to a source familiar with the coaching search.
He would succeed Bill Cowher, who resigned Jan. 5 after 15 seasons as the Steelers' coach.
Tomlin beat out Russ Grimm, 47, a Steelers assistant for six seasons and their assistant head coach for three, who had been considered the front-runner. The other finalist for the job was Chicago Bears defensive coordinator Ron Rivera.
Before joining the Vikings a year ago, Tomlin had spent five years as a defensive coach with the Tampa Bay Buccaneers. Before that, he was a college assistant at Cincinnati, Arkansas State, Memphis and Virginia Military Institute.
Tomlin would become only the third Steelers head coach in 38 years and the NFL's sixth African-American head coach.