The court, in a ruling issued in San Francisco, said, "We affirm the judgment in its entirety."
Davis, 54, was convicted and sentenced to death in Santa Clara County Superior Court in 1996 for abducting Klaas from a slumber party at her mother's home on Oct. 1, 1993, and strangling her.
Klaas' body was found two months later near U.S. Highway 101 in the Cloverdale area after Davis, who had been arrested for a parole violation, led investigators to the location.
Davis' trial was moved from Sonoma County to Santa Clara County because of extensive publicity about the case.
In today's 112-page ruling, the court rejected a series of appeal arguments by Davis, including claims that his trial should have been moved out of the Bay Area and that confessions he gave investigators after being arrested should not have been allowed as evidence.
Justice Joyce Kennard wrote for the court that officers' initial questioning of Davis without a lawyer present was justified by a concept known as the rescue doctrine, because the officers hoped Klaas might still be alive and could be rescued.
Kennard wrote, "So long as she remained missing, her safety was of paramount importance."
Davis' direct appeal to the state high court was the first step in the death penalty appeals process in California.
His lawyer in the appeal, Phillip Cherney, said he will continue appeals by asking for a rehearing and then pursuing a habeas corpus petition in the federal court system.
Cherney said, "We are very disappointed in the California Supreme Court's decision today, though it is hardly unexpected."
The attorney said, "The rule of law that protects us all from overzealous law enforcement agents has taken a severe hit by this decision." Klaas' father, Marc Klaas, said he would have been surprised if the court had not upheld the conviction.
"I was at the trial in 1996 and thought the prosecution and defense did everything as it should be done to bring about justice," Klaas said.
But Klaas said he was "disheartened" that it might take years to resolve Davis' further appeals.
Assistant California Attorney General Ronald Matthias said, "We're very pleased with the outcome."
Matthias said it is impossible to predict how long the additional appeals could take, but said that judging by past cases, it could be "years, not weeks or months."
Davis, who turns 55 tomorrow, had a long criminal record, with previous convictions for burglaries, assault and two kidnappings of women.
His case led to California voters' enactment in 1994 of the state's "three strikes" law, which provides lengthy sentences for repeat offenders.
Davis became a suspect in the case after the owner of a rural Sonoma County property found child's tights, an adult sweatshirt and a hood on Nov. 27, 1993, and told authorities that Davis' car had been stuck on the property on the night Klaas was kidnapped.
Two sheriff's deputies helped Davis free his car that night, not knowing that Klaas, who according to Davis' confession was then still alive, had been left on a nearby embankment.
Davis was arrested on Nov. 30, 1993, at his sister's home in Ukiah.
The court upheld Davis' convictions on a total of 10 counts, including first-degree murder, kidnapping, an attempted lewd act upon a child, robbery and burglary.