During the 1996 season, he led the American League in saves, totaling 43, and appeared in the All-Star Game. During the 1996 World Series, Wetteland recorded four saves and the Yankees won the World Series against the Atlanta Braves in six games. Wetteland won the World Series Most Valuable Player Award, recording the maximum four saves possible during the Series, tying the record for the most saves in a single postseason series (Dennis Eckersley first did it in the 1988 ALCS; since then, Greg Holland matched it in the 2014 ALCS), and setting a record for saves in the full postseason, with 7 (since then, Robb Nen, Troy Percival, Brad Lidge, Koji Uehara, and Holland, share this record). He was awarded with the 1996 Rolaids Relief Man Award.
The Yankees allowed Wetteland to leave as a free agent due to the emergence of Mariano Rivera. He joined the Texas Rangers on December 16, 1996, signing a four-year contract worth $23 million. Before the 1999 season, Wetteland underwent elbow surgery. The surgery robbed him of some of his fastball speed, forcing him to expand his repertoire to include a slider, curveball, and change-up. Wetteland was again named to the All-Star team for the 1999 season, where he pitched a scoreless 9th inning, and became the first Rangers pitcher to earn an All-Star save. His 43 saves that year set a new Rangers record. His final game was on September 20, 2000, and he retired at age 33 after his Rangers contract expired during the 2000 offseason.