The Rangers declined Chafin's 2025 team option Monday.
The Tigers traded Chafin to the Rangers on Tuesday, Jeff Passan of ESPN.com reports.
Chafin (2-1) allowed three runs on two hits and a walk without recording an out to take the loss Friday against the Astros.
Chafin (2-0) tossed 1.1 scoreless innings of relief to earn the win Friday against the Twins.
Chafin recorded two outs in the ninth inning of Friday's 5-4 win over the A's, but he also walked two batters and was pulled for Alex Lange, who recorded the save.
Chafin agreed to a one-year, $4.25 million contract with the Tigers on Sunday, Evan Petzold of the Detroit Free Pressreports.
The Brewers declined Chafin's $7.25 million club option for 2024 on Thursday, Adam McCalvy of MLB.com reports.
The Brewers acquired Chafin from the Diamondbacks on Tuesday in exchange for Peter Strzelecki, Ken Rosenthal of The Athletic reports.
Chafin (2-3) was tagged with the loss and a blown save against the Cardinals on Monday. He allowed five runs on three hits and two walks while striking out two over two-thirds of an inning.
Chafin was activated from the paternity leave list Friday.