Williams, 51, is now scheduled for execution at 0001 (0801GMT) on Tuesday.
On Monday evening, the US Supreme Court refused a stay of execution, as had California’s Supreme Court and a federal appeals court.
A high-profile campaign with celebrity backing has fought to save Williams, who denies four murders in 1979.
With the rejection of his appeal by the US Supreme Court, Williams has exhausted all legal avenues.
He will be executed by lethal injection just after midnight local time at San Quentin prison, north of San Francisco.
Several hundred of his supporters have gathered at the prison gates to protest his innocence, burning candles, beating drums and singing.