Colon would get a $1.75 million, one-year contract if added to the 40-man roster under the terms of the deal agreed to Sunday.
"Bartolo brings a track record of durability and success in the major leagues," Rangers general manager Jon Daniels said in a statement. "He pounds the strike zone and provides quality competition for our rotation."
Colon was a combined 7-14 with a 6.48 ERA in 28 starts for Atlanta and Minnesota last season. He was released by the Braves in July, then signed with the Twins and went 5-6 with a 5.18 ERA in 15 starts for the team.
Colon has 240 career victories in 20 seasons with 10 teams, including the Montreal Expos. The portly right-hander has posted 21 career wins against Texas, the most by any pitcher.
A four-time All-Star, he won the 2005 AL Cy Young Award with the Angels.
Texas was 78-84 last year. Rangers pitchers and catchers are set to hold their first spring workout Feb. 15 in Surprise, Arizona.
Information from the Associated Press was used in this report.