Kubiak's son Klint was named the Vikings' quarterbacks coach, and Brian Pariani. who has worked with Gary Kubiak for more than 20 years, was named tight ends coach.
Kevin Stefanski will remain as the Vikings' offensive coordinator.
Kubiak recently left the Broncos after the team hired Bears defensive coordinator Vic Fangio as its new coach and it was determined Kubiak would not be part of Fangio's coaching staff.
A return to the staff was something John Elway, the president of football operations/general manager, earlier had said was a possibility for Kubiak.
The Broncos fired head coach Vance Joseph on Dec. 31.
Kubiak played in three Super Bowls with the Broncos and won three as an assistant coach with the team in addition to Super Bowl 50, when he was head coach.
Kubiak stepped down after two seasons as the Broncos head coach in January 2017 but remained with the team as an adviser.
His resignation as coach came amid health concerns that arose midway through the season when he was taken from the stadium in an ambulance following a loss and spent a night in the hospital. Kubiak was diagnosed with a "complex migraine condition.''
Three years earlier, when he was coach of the Houston Texans, Kubiak collapsed during halftime of a game, an incident later diagnosed as a transient ischemic attack, or mini-stroke.
In addition to his head-coaching jobs, Kubiak was offensive coordinator for the Baltimore Ravens.