The 36-year-old right-hander was 1-4 with an 8.71 ERA in six spring-training starts for the Padres, allowing 25 runs and 26 hits in 20 2-3 innings. He was 7-6 with a 5.20 ERA in 17 starts and 13 relief appearances for the New York Yankees last year.
An All-Star in 2001 and '02, Garcia is 152-101 with a 4.15 ERA in 14 major league seasons.
Proctor, 36, is 18-16 with a 4.78 ERA in a seven-year career with the Yankees, Dodgers and Braves. Last year, he had 35 saves in the Korean Baseball Organization.
Baltimore said Friday that outfielder Chris Dickerson had been reassigned to its minor league camp.
The Orioles also completed their rotation by picking right-hander Jake Arrieta to start their home opener on April 5.
Manager Buck Showalter chose Arrieta to start the first game in Baltimore for the third straight season. The Orioles play Minnesota at Camden Yards.
Showalter also announced that Rule 5 draft choice T.J. McFarland had made the team. The left-hander will go to the bullpen.
Information from The Associated Press was used in this report.