Fullerton has been widely criticized in recent months over the beating death of Kelly Thomas, a mentally ill homeless man who died following a confrontation with Fullerton police last July.
Two policemen charged in the death, Officer Manuel Ramos and Corporal Jay Cicinelli, were placed on unpaid administrative leave.
Richard Jones is stepping down as mayor, but will remain on the city council's panel.
Fullerton Police Chief Michael Sellers has been on medical leave since August.
