ESPN first reported the news.
"(Davis will) be a valuable addition to our team with his experience and leadership," Broncos general manager John Elway wrote on Twitter.
Davis, 31, is a two-time Pro Bowler in the final year of his contract. His production has dropped off significantly in recent seasons, though it's difficult to discern if that is evidence of a decline or more a product of the decay at the quarterback position in San Francisco.
"He's a huge weapon for our offense," Broncos linebacker Brandon Marshall told NFL Network's Andrew Siciliano on Monday's edition of Around The NFL. "The guy's a speed demon. He's a mismatch for linebackers and safeties, so he's going to help us out tremendously. ... I think he'll fit right in to the chemistry that we have, definitely."
Manning has long had success with pass-catching tight ends, with players like Marcus Pollard, Dallas Clark, Jacob Tamme and Julius Thomas all putting up career-best numbers with the Sheriff. A healthy and motivated Davis could serve as a capable replacement for Thomas, who left the Broncos for the Jaguars in free agency. Expect Davis to effectively replace Owen Daniels, who has looked a step slow this season.
On Monday night Davis went on social media to reflect on his time in San Francisco.
"Thank you 49ers for 10 amazing years. It's been a blessing to play for such an incredible organization. Shout out to all of the coaches, staff, and teammates that made this chapter a very special one in my life. Most of all, a very special thank you to the #49erfaithful family."