Stefanski was rumored to be a finalist after his successful tenure in Minnesota, and he'll now fill the league's final head coaching vacancy.
The 37-year-old coordinated the NFL's eighth-ranked scoring offense in 2019, though his unit finished a more modest 16th in yardage. He became the Vikings' full-time play-caller this year after serving as the interim offensive coordinator late in the 2018 campaign.
Stefanski was reportedly the top choice of Browns executive Paul DePodesta a year ago before the franchise promoted Freddie Kitchens, who was recently fired after one season as head coach.
Current offensive coordinator Todd Monken isn't expected to stay on Stefanski's staff, a source told ESPN's Jeremy Fowler. He's being considered for several college play-calling positions.
Cleveland was linked to a number of candidates while looking for a coach to lead the club to its first playoff appearance since 2002. The Browns were also reportedly considering New England Patriots offensive coordinator Josh McDaniels, Buffalo Bills offensive coordinator Brian Daboll, and Philadelphia Eagles defensive coordinator Jim Schwartz, among others.
Now that a new head coach is in tow, owner Jimmy Haslam will turn his attention to the general manager role. Cleveland could target Vikings assistant GM George Paton, according to Rapoport. Eagles executive Andrew Berry has already been interviewed.
The Browns parted ways with former general manager John Dorsey on Dec. 31 after a disappointing 6-10 campaign.