Keenum agreed to a deal with the Broncos, multiple outlets reported. Mike Klis of 9NEWS reported that the contract is expected to be a two-year deal for at least $36 million.
The deal cannot become official until the new league year begins on Wednesday.
The Broncos were reportedly considering fellow quarterback Kirk Cousins before settling on Keenum, who posted career highs in completions (325), attempts (481), completion percentage (67.6), passing yards (3,547) and touchdowns (22) in 2017.
The 30-year-old started 14 regular-season games and both postseason contests last season while leading the Minnesota Vikings to within one win of the Super Bowl. The former journeyman made $2 million on a one-year deal in 2017.
The Broncos limped to a 5-11 finish in 2017 with an offense that finished the season tied for 26th in scoring. Trevor Siemian, Brock Osweiler and Paxton Lynch combined to complete just 58.7 percent of their passes for 3,668 yards with 19 touchdowns and 22 interceptions for a 73.0 passer rating.
Lynch is under contract and 2017 seventh-round selection Chad Kelly, who is the nephew of Pro Football Hall of Famer Jim Kelly, is also on Denver's roster.
The Broncos -- notably Gary Kubiak -- are familiar with Keenum during his time in Houston in 2013.
Keenum started eight games that season, which wound up being Kubiak's final year as head coach with the Texans. Kubiak has since taken on a role in the Broncos' front office this offseason.