Galaxy officials would not confirm Yallop's departure, but according to a league source, the coach informed the squad of his decision following Sunday's charity match against Hollywood United.
Yallop endured a difficult season in Los Angeles in which he and his players were under the microscope following the arrival of superstar David Beckham. Injuries limited Beckham's impact as the Galaxy made a late playoff push but failed to qualify for Major League Soccer's postseason.
"We are all disappointed to see Frank go," Beckham said. "But he has to do what is best for him and for his family."
Yallop is a huge favorite in the Bay Area, where he helped lead the previous San Jose franchise to two MLS championships in 2001 and 2003. Yallop is expected to be unveiled as the Earthquakes' new boss this week.
On Monday, the Galaxy are due to depart on an exhibition tour to Vancouver, where director of soccer Paul Bravo is likely to lead the team.