NFL Network insider Jason La Canfora reported earlier Wednesday that other general managers around the league expected the Browns to land Musgrave, whose vast experience in the West Coast offense made him a fit for team president Mike Holmgren's philosophy.
Musgrave, the Atlanta Falcons' quarterbacks coach the previous five seasons and their assistant head coach this past year, drew interest from several teams. He interviewed in Cleveland on Tuesday.
Musgrave worked with quarterback Matt Ryan in Atlanta, but he likely appeals to new Vikings coach Leslie Frazier because of his work in the Falcons' run-first system. Frazier has said that running back Adrian Peterson should be the focal point of the Vikings' offense, especially with quarterback Brett Favre not coming back next season.
"The players on the offensive side of the ball are very attractive to be associated with," Musgrave said in a statement released by the Vikings. "I'm looking forward to utilizing their strengths to get fantastic results. The offensive weapons on this squad are impressive."
In Minnesota, Musgrave replaces Darrell Bevell, who interviewed for the same job in Seattle on Wednesday.
Fred Pagac will remain on staff as defensive coordinator.
Johnson also spent nine seasons as a quarterbacks coach, a position the Vikings need to fill after firing Kevin Rogers earlier this month.
"It's a great honor and a tremendous opportunity that I would have a chance to coach with Leslie," Singletary said in a statement released by the Vikings. "He's a quality coach and I know that to be a part of something that he's doing is special. When I look at what they have put together as an organization they have a lot of the pieces in place to do some special things. I'm excited to come there and be a part of that and help take it to the next level."
Priefer spent the previous two seasons running the special teams in Denver. In Minnesota, he'll work with established punter Chris Kluwe and kicker Ryan Longwell, if the latter is re-signed.
"I have kind of been envious of the core special teams guys here in Minnesota," Priefer said. "We had some good players in Denver but I know there are some outstanding players there in Minnesota and I look forward to working with them."
He will have to receive a crash course in current events, however. As part of his statement, Priefer said he was looking forward to playing indoors at Mall of America Field.
"I'm very excited to play at Mall of America Field, especially late in the year," he said. "Having a domed stadium is a definite advantage I think for both teams. You have to look at it as a kicking advantage for your guys that do that every week."
Just one problem -- the Metrodome's roof collapsed under heavy snow in December and has yet to be repaired, leaving some doubt as to where the Vikings will play next season.
The Associated Press contributed to this report.