The foundation on Thursday announced the 58-year-old attorney will become the group's senior adviser and president-elect. Wildcatter Richardson used his fortune to create the foundation to do good works in Texas.
Geren will follow Valleau Wilkie Jr., who retires in 2011 after heading the foundation since 1973. Wilkie is 86.
Geren's stint as Army secretary ended last year.
The Fort Worth Star-Telegram reported Friday that Geren will earn about $350,000 as foundation president, nearly twice as much as his salary at the Pentagon.