The move was announced Wednesday, more than five months after Dyson was traded to the Giants for a player to be named later. Texas also paid about $1.5 million to cover some of Dyson's remaining salary.
Cole hit .249 with seven homers and 34 RBI in 83 games with Double-A Richmond this year. The 25-year-old outfielder spent part of the season on the disabled list with a right oblique injury.
Dyson was traded June 6, less than a week after being designated for assignment by the Rangers. Dyson had lost his role as closer in Texas, where he was 1-6 with a 10.80 ERA in 17 appearances before going 3-4 with 14 saves and a 4.03 ERA in 38 games for the Giants.