Chirinos and Frazier both got contracts that included club options for 2021. The deals were announced by the team Wednesday.
Left-handed pitchers Kyle Bird and Jeffrey Springs were designated for assignment to clear spots on the 40-man roster. The Rangers have seven days to trade, release, or outright the players to the minor leagues.
The 35-year-old Chirinos gets a $5.5 million salary this season, and his deal includes a $6.5 million club option for 2021 that includes a $1 million buyout.
Frazier will make $3.5 million, and the Rangers have a $5.75 million option on the two-time All-Star for 2021 with a $1.5 million buyout.
After Chirinos played 442 games with the Rangers from 2013-18, the team declined a $4.5 million option and he became a free agent. He spent last season on a $5.75 million deal with AL West rival Houston, where he caught AL Cy Young winner Justin Verlander and runner-up Gerrit Cole. Chirinos homered in Game 3 and Game 4 of the World Series.
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 instead signed with the division rival Los Angeles Angels.
Six different players started games at third base last season for the Rangers. Adrian Beltre, a four-time All-Star and five-time Gold Glove third baseman who had 3,166 career hits, played the last eight of his 21 big league seasons in Texas before retiring after the 2018 season.
Frazier, who turns 34 on Feb. 12, spent the past two seasons with the New York Mets, hitting .251 with 21 homers last year. He is a .243 career hitter that also played for the Cincinnati Reds (2011-15), the Chicago White Sox (2016-17) and Yankees (2017). He has started at third base in 1,000 of his 1,186 career games.