The U.S. Supreme Court denied an appeal filed Monday evening, his last recourse for reversing his death sentence.
The death penalty of Williams, 51, should proceed as planned at 3:01 a.m. EST (12:01 PST) at San Quentin State Prison. Williams will be executed for murdering four people in two 1979 holdups.
Williams has consistently denied committing the gruesome killings, but has apologized for forming the notoriously bloodthirsty gang.
"Is Williams' redemption complete and sincere, or is it just a hollow promise?" Schwarzenegger wrote less than 12 hours before the execution. "Without an apology and atonement for these senseless and brutal killings, there can be no redemption."
Late Sunday, the California Supreme Court refused to grant a stay of execution. Williams filed an application for a stay of execution and a petition for writ of habeas corpus with the U.S. Supreme Court Monday evening, after the governor announced his decision to deny clemency.
Schwarzenegger was unswayed by pleas from Hollywood stars and petitions from more than 50,000 people who said that Williams had made amends during more than two decades in prison by writing a memoir and children's books about the dangers of gangs.
"After studying the evidence, searching the history, listening to the arguments and wrestling with the profound consequences, I could find no justification for granting clemency," Schwarzenegger said. "The facts do not justify overturning the jury's verdict or the decisions of the courts in this case."
Schwarzenegger could have commuted the death sentence to life in prison without parole.
The city of Los Angeles prepared for angry protests after the California governor made his announcement.
"Too often I hear the governor and many who are around him talk about his values system," said NAACP President Bruce S. Gordon. "In this particular case, those values seem to be cast aside. There is absolutely no recognition given to redemption."
Williams' fate became one of the nation's biggest death-row cause-celebres in decades.
Prosecutors and victims' advocates contended Williams was undeserving of clemency from the governor because he did not own up to his crimes and refused to inform on fellow gang members.
They also argued that the Crips gang Williams co-founded in Los Angeles in 1971 is responsible for hundreds of deaths, many of them in battles with the rival Bloods for turf and control of the drug trade.
Williams stood to become the 12th California-condemned inmate executed since lawmakers reinstated the death penalty in 1977 after a brief hiatus.
He was condemned in 1981 for gunning down convenience store clerk Albert Owens, 26, at a 7-Eleven in Whittier and killing Yen-I Yang, 76, Tsai-Shai Chen Yang, 63, and the couple's daughter Yu-Chin Yang Lin, 43, at the Los Angeles motel they owned.
Williams claimed he was innocent. The California Supreme Court, a federal district court judge in Los Angeles, the 9th U.S. Circuit Court of Appeals and the U.S. Supreme Court have all upheld his convictions.
The last time a California governor granted clemency was in 1967, when Ronald Reagan spared a mentally infirm killer. Schwarzenegger — a Republican who has come under fire from members of his own party as too accommodating to liberals — has rejected clemency twice before during his two years in office.
In denying clemency to Williams, Schwarzenegger said that the evidence of his guilt was "strong and compelling," and he dismissed suggestions that the trial was unfair.
Schwarzenegger also pointed out the brutality of the crimes, noting that Williams allegedly said about one of the killings, "You should have heard the way he sounded when I shot him."
According to the governor's account, Williams then made a growling noise and laughed for five to six minutes.
Williams' supporters say he has redeemed himself by speaking out against violence and writing children's books on the evils of gang life.
During his 24 years at San Quentin, the Crips street gang founder turned his life around to the point that a Swiss legislator, college professors and others repeatedly submitted his name for Nobel peace and literature prizes.
But the governor noted that Williams dedicated his 1998 book "Life in Prison" to a list of figures that included the black militant George Jackson — "a significant indicator that Williams is not reformed and that he still sees violence and lawlessness as a legitimate means to address societal problems."
Schwarzenegger also noted that there is "little mention or atonement in his writings and his plea for clemency of the countless murders committed by the Crips following the lifestyle Williams once espoused. The senseless killing that has ruined many families, particularly in African-American communities, in the name of the Crips and gang warfare is a tragedy of our modern culture."
Williams' supporters, an outspoken group ranging from community leaders to actors and rappers, have held rallies in his support and argue that executing him would send the wrong message.
Among the celebrities who took up Williams' cause were Jamie Foxx, who played the gang leader in a cable movie about Williams; rapper Snoop Dogg, himself a former Crip; Sister Helen Prejean, the nun depicted in "Dead Man Walking"; Bianca Jagger; and former "M..A..S..H" star Mike Farrell.
"If Stanley Williams does not merit clemency," defense attorney Peter Fleming Jr. asked, "what meaning does clemency retain in this state?"
Williams spent Monday morning in the prison's special visiting room with his legal team, supporters and friends, San Quentin spokesman Vernell Crittendon told reporters. Among his visitors were the Rev. Jesse Jackson.
Crittendon said Williams has been quiet and cooperative and will be moved into a special holding cell adjacent to the execution chamber at 9 p.m. EST (6 p.m. PST), where he will be served his last meal if he wants one at about 10:30 EST (7:30 PST).
The 5,500 other inmates at the prison have been under modified lockdown since just after midnight local time on Monday, according to Crittendon, and were in full lockdown as of 2 p.m. — meaning they must stay in their cells at all times. They'll remain that way until normal operations resume at San Quentin at approximately 9 a.m. Tuesday.
The impending execution resulted in feverish preparations over the weekend by those on both sides of the debate, with the California Highway Patrol planning to tighten security outside the prison.
A group of about three dozen death penalty protesters were joined by the Rev. Jackson as they marched across the Golden Gate Bridge after dawn Monday en route to the gates of San Quentin, where they were expected to rally with hundreds of people.
At least publicly, the person apparently least occupied with his fate seemed to be Williams himself.
"Me fearing what I'm facing, what possible good is it going to do for me? How is that going to benefit me?" Williams said in a recent interview. "If it's my time to be executed, what's all the ranting and raving going to do?"
FOX News' Catherine Donaldson-Evans and The Associated Press contributed to this report.