The Rays, in turn, receive top infielder prospect Christian Arroyo and minor league pitchers Matt Krook and Stephen Woods. Tampa Bay also must take on the last year of outfielder Denard Span's contract, which is for $9 million.
Britton's injury will require surgery on Thursday in California to be performed by Dr. Ken Jung.
Major League Baseball commissioner Rob Manfred defended the new Miami Marlins ownership group, in particular Derek Jeter, during an interview on ESPN radio.
Manfred went on the Dan Le Batard show, which is based in Miami, and fielded questions about the Marlins trading away All-Stars Giancarlo Stanton, Marcell Ozuna and Dee Gordon, and the general direction of the team under Jeter's ownership group.
The Seattle Mariners officially signed free-agent right-handed relief pitcher Juan Nicasio to a two-year contract, the team announced.
Financial terms were not disclosed by the team, but the Seattle Times reported the deal was for a total of $17 million.
Nicasio, 31, pitched in a career-high 76 games in 2017 with three different teams -- Pittsburgh (65), Philadelphia (two) and St. Louis (nine) -- finishing with a combined 5-5 record, six saves and a 2.61 ERA.
The Milwaukee Brewers and free-agent right-hander Jhoulys Chacin reached an agreement on a two-year contract, multiple outlets reported.
Chacin joins Yovani Gallardo as the second free-agent pitcher to sign with the Brewers over the past week. Gallardo is rejoining his former team after struggling in one season apiece with the Baltimore Orioles and Seattle Mariners, respectively.
The Los Angeles Dodgers started the process of restocking their bullpen by signing right-hander Tom Koehler to a one-year contract on Wednesday.
Koehler, 31, who was non-tendered by Toronto, is 36-55 with a 4.39 ERA in 161 major league games with Miami (2012-17) and the Blue Jays (2017).