The 45-year-old Geren was a catcher for parts of five seasons with the New York Yankees and San Diego Padres, and has been on the A's coaching staff for the last four seasons after joining the organisation as a minor league manager in 1999.
He will replace the fired Ken Macha as manager of the defending AL West champions after compiling a 452-390 record in seven seasons as a minor league manager.
"I'm just thrilled to death to do it," Geren said. "I'm not going to make a lot of changes, as we had a team that had a lot of success last year."
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Colorado bench coach Jamie Quirk and former major league pitcher and pitching coach Orel Hershiser were also interviewed for the job.
Geren is close friends with A's general manager Billy Beane, who was unable to attend the press conference announcing his hiring due to a death in his family.
Macha was fired after four seasons on October 16, two days after Oakland was eliminated in the AL Championship Series by the Detroit Tigers.
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