The deal is pending a physical.
Mathis, who turns 36 in March, is regarded as one of the game's top defensive catchers. That has made up for his shortcomings at the plate, where he's just a .198 career hitter.
The Rangers were in need of a catcher after declining the 2019 option for Robinson Chirinos. Their primary starting catcher had a $4.5 million option for the 2019 season with a $100,000 buyout.
Texas will be Mathis' fifth major league team. He previously spent seven seasons with the Angels (2005-11), one with the Blue Jays (2012), four with the Marlins (2013-16) and the past two with the Diamondbacks.