According to the report, the Rockies will give Davis a three-year deal, worth $52 million, making him the highest paid reliever in baseball in terms of annual average salary.
The deal includes a fourth-year vesting option that could potentially earn Davis up to $66 million.
Davis, 32, spent last season with the Chicago Cubs and went 4–2, with a 2.30 ERA, 1.142 WHIP, 32 saves and 79 strikeouts in 58 2/3 innings.
Before his Chicago stint, he spent four seasons each with the Tampa Bay Rays and the Kansas City Royals, helping the Royals win the 2015 World Series.
Davis' signing boosts a Colorado bullpen that ranked third in the National League with 47 saves and was tops in the league in the fewest blown saves.