A group headed by local businessman Ted Lerner bought the franchise from Major League Baseball for $450 million in May, with the approval of Commissioner Bud Selig.
The announcement about Bowden's future was made late Friday by incoming team president Stan Kasten.
No terms were disclosed.
"I look for Jim to be here for a very long time," Kasten said on the team's Web site. "I want people to regard a GM as permanent, part of the fabric of creating the long-term plan."
Bowden has been running the franchise since it relocated from Montreal last year. There had been extensive speculation about his future.
The Washington Post reported that he will be the GM at least through October, when his deal with baseball expires.
No mention was made about the status of Manager Frank Robinson.