Financial terms were not disclosed.
The 32-year-old Glanville spent the last five seasons with the Phillies but was not offered salary arbitration earlier this month.
"Doug Glanville provides us with a quality defensive center fielder who has the potential to be an everyday player," Rangers General Manager John Hart said. "He has been a good offensive player and baserunner throughout his career and could also be a candidate to hit at the top of the lineup. His addition improves our depth in the outfield."
Glanville has seen his average decline in each of the last three years. He batted .249 with six homers and 29 RBI in 2002.
Glanville had his best season in 1999, when he hit .325 with 11 homers and 73 RBI. He has a .281 career average with 52 homers, 303 RBI and 156 stolen bases in 948 games with the Chicago Cubs and Philadelphia.
Since Glanville was not offered arbitration, the Phillies will not receive compensation.