Also hired on Wednesday was former Cleveland Browns linebackers coach George Edwards, LSU defensive line coach Travis Jones and 49ers defensive line coach Dan Quinn.
On the other side, Clarence Brooks, who coached the Dolphins defensive line last year, left to take the same position with the Baltimore Ravens.
The biggest remaining piece in the coaching staff puzzle is a defensive coordinator, and it is widely believed the choice is New England linebackers coach Dean Pees, whom the Dolphins can't hire until the Patriots' season is over.
That's a similar scenario to that involving Linehan, who became available after the Vikings were eliminated by Philadelphia in the divisional playoffs last Sunday.
"Scott is the person we targeted as our first choice to be our offensive coordinator, but we had to wait until the Vikings finished their season," head coach Nick Saban said in a statement. "He did an outstanding job in Minnesota and they had one of the most effective offenses in the league.
"His expertise is not only in developing good offensive systems, but also in raising the level of play of his quarterbacks everywhere he has been. We're pleased he has joined our staff and he will be a great asset to the football team."