The move increases the chances that Minnesota will sign free-agent quarterback Kirk Cousins to take over since Denver had been one of four suitors for him.
He played with Houston in 2014, St. Louis in 2015, Los Angeles in 2016, Minnesota in 2017 and will now head to Denver in 2018.
He threw for 3,547 yards, 22 touchdowns and just seven interceptions, helping the Vikings reach the NFC Championship Game.
The 30-year-old Keenum is considered the second-best QB available on the open market. Kubiak is now the Denver Broncos' senior personnel advisor so the team will be familiar with their new quarterback.
But the Broncos are desperate to get back to contender status after slumping to a record of 5-11 in a 2017 season in which they tried Trevor Siemian, Paxton Lynch and Brock Osweiler at quarterback.
Keenum will join a Broncos squad that ranked 27th out of the 32 teams with 18.1 points per game.
Six years ago, GM John Elway landed Peyton Manning, the biggest free-agent prize in National Football League history, following his release by the Colts and a series of neck fusion surgeries. "That is what we are working on". "Obviously, we have to get better at that position". Now they will count on Keenum to get them back into the playoffs and, they hope, be in the mix to advance deep into the postseason. There were some things that we should have done, that we should have done differently that we didn't do.