The Rays also received top shortstop prospect Daniel Robertson, minor league outfielder Boog Powell and cash considerations.
Tampa Bay announced later Saturday that it has finalized a one-year, $7.5 million deal with veteran infielder Asdrubal Cabrera, who spent last season with the Cleveland Indians and Washington Nationals.
Zobrist, 33, has spent his entire nine-year career with the Rays and has significant playing time at several positions, including second base, shortstop and right field. The two-time All-Star batted .272 with 10 home runs and 52 RBIs last season.
"It's an emotional and meaningful day as we bid farewell to Ben Zobrist and thank him for everything he's meant to the Rays organization," Rays president of baseball operations Matt Silverman said in a statement released by the team. "Any description of his value, talent and character would understate how we feel about Ben, and we consider ourselves fortunate for all our great moments together."
Escobar batted .258 with seven homers last season, his second with Tampa Bay and his eighth in the majors.
Jaso appeared in 99 games last season for Oakland, batting .264 with nine homers and 40 RBIs.
Robertson, 20, was a first-round draft selection of the Athletics in 2012 and batted .310 with 15 homers at Class A Stockton last season.
Powell, who is not related to former Baltimore Orioles slugger Boog Powell, batted .343 while splitting last season between Stockton and Class A Beloit.