Talib was placed on injured reserve earlier this month with fractured ribs but is expected to be ready to return by Week 15, the earliest he will be eligible to play per league rules.
He becomes the second high-profile cornerback dealt by the Rams this season, joining Marcus Peters who was traded to the Baltimore Ravens two weeks ago. The Rams immediately replaced Peters by acquiring star cornerback Jalen Ramsey in a trade with the Jacksonville Jaguars.
The trade of Talib will help free up salary cap space to possibly sign Ramsey to a long-term contract extension.
Talib, 33, is a five-time Pro Bowl selection with 35 interceptions (returning 10 for touchdowns) since being selected in the first round (20th overall) of the 2008 draft by the Tampa Bay Buccaneers. He also has played for the New England Patriots and Denver Broncos, with whom he won a Super Bowl ring after the 2015 season.
He will become an unrestricted free agent after this season.