The teams announced the trade Saturday. Tampa Bay also got infielder Daniel Robertson, outfielder Boog Powell and cash in the trade.
The 33-year-old Zobrist is a two-time All-Star. He hit .272 with 10 home runs and 52 RBIs last season, and made starts at second base, shortstop, all three outfield spots and designated hitter.
Escobar batted .258. The 32-year-old shortstop had seven homers and 39 RBIs.
Jaso hit .264 with nine home runs and 40 RBIs. The 31-year-old went on the disabled list on Aug. 25 because of a concussion and missed the rest of the season.
The A's have been active since winning a wild-card slot last season. They've traded stars Josh Donaldson and Jeff Samardzija and made several other moves.