Bobby Evans, Giants vice president of baseball operations, said the players agreed on one-year, non-guaranteed major league contracts.
Others in the group with zero to three years service time are reliever Dan Runzler, shortstop Brandon Crawford, catchers Hector Sanchez and Chris Stewart, pitcher Eric Surkamp, and first basemen Brandon Belt and Brett Pill.
Posey is returning from a season-ending leg injury from a home-plate collision May 25 with the Marlins' Scott Cousins. He played in his first Cactus League game Friday.
The 22-year-old Bumgarner went 13-13 with a 3.21 ERA in 204 2-3 innings last year in his first full season as a starter for San Francisco. He pitched eight shutout innings in Game 4 of the 2010 World Series against Texas as the Giants went on to capture their first championship since moving West in 1958.
Other players agreeing Friday: pitchers Hector Correa, Steve Edlefsen and Danny Otero; infielders Ehire Adrianza, Charlie Culberson, Conor Gillaspie and Angel Villalona; and outfielders Tyler Graham, Roger Kieschnick and Francisco Peguero.