Padilla was 9-12 with a 4.71 ERA in 27 starts last season in Philadelphia. He was traded July 26, 2000, from Arizona to the Phillies along with three other players for pitcher Curt Schilling. Padilla made $3.2 million last year and is eligible for salary arbitration.
Padilla was an All-Star in 2002, when he was 14-11 with a 3.28 ERA, and he followed that by going 14-12 with a 3.62 ERA in 2003. He is just 16-19 over the past two seasons, missing more than two months in 2004 because of right elbow tendinitis.
"He is a youthful starting pitcher with an excellent track record that includes an All-Star selection and will bolster our starting rotation," Rangers general manager Jon Daniels said.
Morris turned down a $25 million, three-year offer from the Rangers, and the free agent instead agreed to a three-year deal Monday with the San Francisco Giants. The Rangers were willing to trade All-Star third baseman Hank Blalock to get Beckett, but the Marlins last month traded Beckett to Boston.
After the Rangers cut ties with 41-year-old All-Star left-hander Kenny Rogers, the only returning starting pitchers for Texas were rookies last season. Chris Young was 12-7 with a 4.26 ERA in 31 starts, while Kameron Loe (9-6, 3.42 ERA in 48 games/eight starts) and Juan Dominguez (4-6, 4.22 in 22 games/10 starts) finished the season in the rotation.
The 28-year-old Padilla is 51-51 with a 3.95 ERA in 194 career games (111 starts) over seven seasons with the Diamondbacks (1999-2000) and Philadelphia. Rangers manager Buck Showalter was in Arizona when Padilla had a 3.35 ERA in 35 games as a reliever there.
Omar Daal, Nelson Figueroa and Travis Lee -- the rest of the Arizona players involved in the Schilling trade -- previously left the Phillies.