The rejection on Monday came after two court appeals were also denied and clears the way for Williams to be executed by lethal injection at 12.01am (0801 GMT) on Tuesday for murdering four people in two robberies in Los Angeles in 1979.
Schwarzenegger wrote: "Stanley Williams insists he is innocent, and that he will not and should not apologise or otherwise atone for the murders of the four victims in this case.
"Without an apology and atonement for these senseless and brutal killings there can be no redemption.
"Based on the cumulative weight of the evidence, there is no reason to second-guess the jury's decision of guilt or raise significant doubts or serious reservations about Williams's convictions and death sentence."
Death penalty debate
The case has generated widespread interest and fierce debate over the death penalty in the United States because Williams, 51, has written a series of books warning young people against gangs and says he has found redemption.
His supporters argued he should have been spared so that he could continue his anti-gang work from behind bars.
"In this case, the one thing that would be the clearest indication of complete remorse and full redemption is the one thing Williams will not do"
Alice Huffman, president of the California National Association for the Advancement of Coloured People, said: "We are deeply saddened by the governor's decision. We believe this is a serious blow to our effort to fight gangs."
Schwarzenegger, politically weakened by a loss on all his initiatives in a special election he called last month, would have risked alienating his Republican Party if he granted clemency.
He wrote: "In this case, the one thing that would be the clearest indication of complete remorse and full redemption is the one thing Williams will not do."
At San Quentin State Prison, north of San Francisco, a spokesman described Williams as quiet and cooperative on what is likely to be his last day alive.
On Monday, the US 9th Circuit Court of Appeals rejected the latest appeal by lawyers to reconsider the case.
Ronald George, the California Supreme Court's chief justice, told Reuters last week that there was "something wrong" with a system in which judges must routinely ponder last-minute death-row filings after two decades of decisions.
Williams's lawyers said they would appeal to the US Supreme Court and ask Schwarzenegger again for a stay of execution.
The scheduled execution comes just over a week after a double murderer became the 1000th prisoner to be executed in the US since the re-imposition of capital punishment in 1976.
"I am not the kind of person to sit around and worry about being executed. I have faith and if it doesn't go my way, it doesn't go my way"
Stanley Tookie Williams
Williams was convicted in 1981 of killing Albert Owens as he lay face down on the floor of a convenience store in a $120 robbery.
Two weeks later, Williams shot dead an elderly Taiwanese immigrant couple running a motel.
In a Reuters interview last month, Williams said: "I am not the kind of person to sit around and worry about being executed. I have faith and if it doesn't go my way, it doesn't go my way."
Williams has said he did not commit the murders, but said he hurt many people as leader of the notorious Crips street gang in the Los Angeles area.
Williams has attracted a number of high-profile backers, including Jamie Foxx, who starred in a sympathetic made-for-TV movie about the case.
Opponents of clemency said Williams continues to have ties to the Crips gang he says he co-founded.