The teams also exchanged draft picks with a fifth-round pick headed to Miami and a 2022 seventh-rounder headed to Los Angeles.
For the winless Dolphins, this move is essentially to buy a draft pick, as Talib is currently on injured reserve. The Rams were looking to dump Talib's salary; there is approximately $4.2 million left on his deal. Talib will be an unrestricted free agent after this season.
Dolphins general manager Chris Grier alluded on Sunday to a willingness to make this sort of move. One of the biggest priorities of the Dolphins' rebuild is collecting draft picks to add talent in the 2020 and 2021 drafts.
"We're getting calls, like every team, and then there's teams calling us too, trying to unload players as well," Grier said Sunday. "We might be [a buyer], yeah. There's some things that might tempt us. We've had some conversations with teams."
The Dolphins are set to have 14 picks in the 2020 draft, including three first-round picks, two second-round picks and two projected compensatory picks.
The Rams put Talib on IR earlier this month, citing a rib injury suffered in Week 5 against the Seattle Seahawks. Talib could return by Week 15, although it remains uncertain whether he will play again this season.
Talib is the second starting cornerback the Rams have traded in the past two weeks. They sent Marcus Peters to the Baltimore Ravens for linebacker Kenny Young and a fifth-round pick, then immediately completed a blockbuster trade for Jalen Ramsey, sending first-round picks in 2020 and 2021 and a fourth-round pick in 2021 to the Jacksonville Jaguars to acquire the star corner.
By trading Talib, the Rams clear up salary-cap space to possibly sign Ramsey to a long-term contract extension.
In five games, Talib had two pass deflections and seven tackles, playing in a secondary that had underwhelming results before the team engaged in a series of trades after Week 6.
"Everything we do, we do in the best interest of the team, long term and short term," Rams coach Sean McVay said Tuesday. "... Nothing but a lot of great things from our end on Aqib and what he's meant to us."
If Talib does end up playing for Miami in Week 15 or later, it will be a good opportunity for coach Brian Flores to see whether the veteran cornerback would be worth re-signing after the season. The Dolphins play a heavy man-to-man scheme, which is Talib's biggest strength, and he could be an asset for star cornerback Xavien Howard, who has a similar style. Like Talib, Howard is now going on IR; the Dolphins put him there with a knee injury Tuesday, a source confirmed to ESPN.
But the main priority here for Miami is the draft pick. The Dolphins made a similar move over the summer, trading quarterback Ryan Tannehill and a sixth-round pick to Tennessee for a fourth-round pick while paying a portion of Tannehill's contract -- essentially buying a pick.
Talib, 33, is a five-time Pro Bowl selection with 35 interceptions (returning 10 for touchdowns) since being selected in the first round of the 2008 draft by the Tampa Bay Buccaneers. He is tied for first among active NFL players in interceptions and is fourth all time in pick-sixes. He also has played for the New England Patriots and Denver Broncos, with whom he won a Super Bowl ring after the 2015 season.
The Rams acquired Talib in a trade with the Broncos before the 2018 season, sending a fifth-round pick to Denver.
Flores has familiarity with Talib from when both were with the Patriots.
"I have some history with Aqib. I think he's a really good player," Flores said Tuesday. "We had an opportunity to acquire him and some draft capital, so we felt like that was the best move for us."