The Broncos will receive a fifth-round pick in the 2018 draft for Talib, a source told ESPN's Adam Schefter. The trade won't become official until the new league year begins Wednesday.
Talib wanted to play for defensive coordinator Wade Phillips in L.A. or Bill Belichick in New England, sources told Schefter. The idea of playing elsewhere was not something he found desirable. This helped dictate the trade to the Rams, the sources said.
Since he entered the league as a first-round pick by the Tampa Bay Buccaneers in 2008, Talib has the most interceptions by a cornerback in the NFL (34) and his 10 career interceptions for touchdown rank fourth all time.
Talib returned his only interception this past season 103 yards for a touchdown in the Broncos' Week 2 victory over the Dallas Cowboys.
But Talib got caught between the Broncos' need for additional salary-cap space and the team's belief that cornerback Bradley Roby is ready to be a starter.
The Broncos certainly got their money's worth from the 32-year-old cornerback. Talib was signed to a six-year, $57 million deal in 2014 and was named to the Pro Bowl in each of his four seasons with the team. Talib had 11 interceptions combined over the past four seasons and he was at least tied for the team lead in three of those seasons.
Talib was also suspended for a game on two separate occasions in his time with the Broncos, for poking then-Indianapolis Colts tight end Dwayne Allen in the eye during a 2015 game and for a fight with Raiders receiver Michael Crabtree during the Broncos' loss in Oakland this past season.
Talib also missed the Broncos' visit to the White House in the summer of 2016 because he had suffered a gunshot wound to his lower right leg in Dallas. No charges were filed in the incident -- the bullet entered Talib's leg near his thigh and exited his right calf.
He did not have surgery after the incident, and at the time there were reports, unconfirmed by Dallas police, that police had determined Talib shot himself.
He was named captain by his teammates this past season; it was the first time in his career he had been selected as a team captain.
For the Rams, the Talib acquisition continues what has already been a busy offseason. They previously acquired All-Pro cornerback Marcus Peters from the Kansas City Chiefs, then sent outside linebacker Robert Quinn to the Miami Dolphins and inside linebacker Alec Ogletree to the New York Giants.
Talib and Peters, who have combined for seven Pro Bowls and two first-team All-Pro nods, will now be the Rams' starting cornerbacks on the outside. Kayvon Webster, who's recovering from a ruptured Achilles tendon he suffered in December, and Sam Shields, signed earlier Thursday after missing most of the past two years with concussions, can serve as depth alongside Troy Hill, who stepped up down the stretch last season.
The Rams also want to bring back Nickell Robey-Coleman, who excelled at slot corner. But they are now guaranteed to not bring back Trumaine Johnson, who spent the past two seasons playing under the franchise tag -- set at $16.7 million last season -- and now promises to have a robust market in free agency. The Rams will probably get a third-round compensatory pick in next year's draft by letting Johnson sign elsewhere.
Talib and Peters are both signed through 2019 and would combine to cost about $30 million during that time.
ESPN's Jeff Legwold and Alden Gonzalez contributed to this report.