The deal, which is pending a physical, includes a team option for the 2021 season, sources said. If the option is exercised, Frazier would make $9.25 million over two years.
Third base is a primary need for the Rangers, who lost out in their pursuit of top free agent Anthony Rendon this offseason when the Texas native signed with the division rival Los Angeles Angels. Frazier also provides a right-handed hitter in the middle of a left-leaning lineup, and he could play first base if Texas adds other players.
Adrian Beltre, a four-time All-Star and five-time Gold Glove third baseman who had 3,166 career hits, retired after the 2018 season. He played the final eight of his 21 big league seasons with Texas.
The Rangers added veteran Asdrubal Cabrera last offseason, and he hit .235 while starting 90 games before being released at the end of July. He then signed with the Washington Nationals and played second base while part of their World Series run, along with Rendon.
Five other players started games at third base for Texas last season.
Frazier, a two-time All-Star in eight major league seasons, hit .251 with 21 home runs and 67 RBIs in 133 games last season for the New York Mets.
He is a career .243 hitter with 214 home runs and 624 RBIs.
Frazier was an All-Star in 2014 and 2015. He hit 35 homers for the Cincinnati Reds in 2015 and won the Home Run Derby, then set career highs with 40 homers and 98 RBIs for the Chicago White Sox in 2016.
Frazier, who is from New Jersey, was a 1998 Little League World Series champion in Toms River and later starred at Rutgers.
The Associated Press contributed to this report.