The Broncos agreed with Welker on a two-year contract worth $12 million, a league source told ESPN NFL Insider Adam Schefter. The deal also includes $150,000 in incentives in each year if he catches 90 passes.
The other team that pursued Welker was the Tennessee Titans, a source familiar with the situation said.
The Patriots responded quickly to Welker's loss by agreeing in principle on a five-year, $31 million deal, including $10 million guaranteed, with St. Louis Rams wide receiver Danny Amendola, a league source told Schefter.
As for how Welker's departure has been received by Brady, who last month restructured his contract to provide more salary-cap flexibility to help the Patriots build a better team, a source who had direct contact with Brady told ESPNBoston.com that the quarterback is "bummed out."
Broncos executive vice president of football operations John Elway tweeted the club's agreement with the former New England Patriot.
"Excited to have Wes join the Broncos. His production & toughness will be a great asset!" Elway wrote.
Elway also was thrilled at getting Welker for another reason.
"Any time you can take a player from a team you have to compete against, it helps, especially the caliber of Wes Welker," Elway said. "New England is there year in and year out, and that's a team we have to beat to get where we want to get."
Broncos coach John Fox also was ecstatic at giving Manning another target.
"You try to surround your quarterback with weapons," Fox said Wednesday afternoon outside his Dove Valley office. "I think we took a big step in signing Wes Welker."
"When you're a passing attack and you've got [No.] 18, you're looking for three productive guys out there," Fox said. "I think Wes Welker has proven as productive a slot receiver as there is really in recent NFL history."
The Patriots had been negotiating with Welker leading up to free agency, but the sides could not find common ground on a deal. Welker, 31, played under the franchise tag and a $9.5 million salary for the 2012 season and finished with a team-high 118 catches for 1,354 yards and six touchdowns.
The team elected not to tag him this offseason. If it had, Welker would have received an escalated salary of $11.4 million for the 2013 season.
Welker, the NFL's premier slot receiver, had been a fan favorite in New England since he arrived via trade in 2007. His 672 receptions over six seasons (an average of 112 per season) since joining the Patriots are the most in the NFL during that span. He became the first player in NFL history with five 100-catch seasons.
Among Welker's biggest supporters was Brady, who helped the Patriots clear $15 million in cap space over the next two seasons by restructuring his deal and signing an extension.
Brady was willing to accept the deal, considered below market value, because of the trust that exists between the two-time Super Bowl MVP and the team. Brady felt that in giving New England this cap flexibility, a source told ESPNBoston.com, he trusted the Patriots would add the right players to finish his career with the best chance to win another championship.
On Monday, Patriots owner Robert Kraft said he hoped Welker would be "a Patriot for life, just like Tom Brady."
The loss of Welker caught some in the Boston area a little bit by surprise.
"Say it ain't so, Wes!" Celtics coach Doc Rivers said before their game against Toronto. "He was fun to watch."
Welker had a team-high eight catches for 117 yards in New England's 28-13 AFC Championship Game loss to the Baltimore Ravens.
Denver was not finished after signing Welker, also agreeing to terms with cornerback Dominique Rodgers-Cromartie and linebacker Stewart Bradley on one-year contracts and defensive tackle Terrance Knighton on a two-year deal.
Last year, the Broncos won the high-stakes contest to sign Manning, prompting Broncos boss Elway to quip, "Plan B? I don't have a Plan B. We're going with Plan A."
Coming off a 13-3 season during which the Broncos looked like a Super Bowl contender before losing to Baltimore in the divisional round of the playoffs, Elway is clearly on the same path this time.
He picked up the league's most productive receiver to play in the slot, where Brandon Stokley was last season. He has been selected to the Pro Bowl in each of the past five seasons and was an All-Pro four of the past five.
Information from ESPN NFL Insider Adam Schefter, ESPNBoston.com's Mike Reiss and Field Yates and The Associated Press was used in this report.