The deal runs through the 2022 season, and the Rangers have options for 2023 and 2024 -- the first two seasons after the right-hander would be eligible for free agency.
First-year manager Chris Woodward tabbed the hard-throwing Leclerc as the team's closer in January.
Leclerc, 25, emerged as Texas' most effective reliever last season, going 2-3 with a 1.56 ERA and 12 saves in 59 appearances. He took over as the Rangers' closer in August after Keone Kela was traded to the Pittsburgh Pirates and was dominant down the stretch, closing out the season with 32 strikeouts over 21 scoreless innings.
He led big league relievers with a .126 opponents' batting average.
The Associated Press contributed to this report.