Brown's suit says the Boston-based bank has spent eight years "raiding" the California Public Employees Retirement System and the California State Teachers' Retirement System pension funds by illegally overcharging fees and penalties for carrying out foreign currency trades.
Whistleblowers brought the allegations to the state's Department of Justice.
The suit seeks to recover $200 million in damages from State Street.
Brown described the allegations as "very profitable, very wrong and now very expensive based on our lawsuit."
In a statement, State Street Bank spokeswoman Carolyn Cichon said, "We categorically deny any allegations of wrongdoing and will defend ourselves against any litigation."