The court's Friday decision is not final, however. Peru's justice minister and Cabinet must endorse it, said the lawyer, Maximo Altez.
Van der Sloot, 24, faces extortion and mail fraud charges in Alabama in connection with the unsolved 2005 disappearance of American teen Natalee Holloway in Aruba exactly five years before he killed Peruvian college student Stephany Flores, who he met in a Lima casino.
The Dutchman, who was raised in Aruba, remains the prime suspect in the Holloway disappearance there, and the U.S. charges stem from his alleged acceptance of $25,000 in early 2010 in exchange for an unfulfilled promise to lead her mother's lawyer to the body.
Federal prosecutors in Birmingham, Ala., where Van der Sloot is charged, declined comment on the court's decision.
Altez told The Associated Press that the Supreme Court's decision follows a pattern in Peru "because there are various people in the same situation and they will all be extradited when they finish their sentences. There's no reason Joran van der Sloot should be different."
Van der Sloot is appealing his sentence and the Supreme Court said that if the appeal is successful he could be extradited immediately thereafter.
Altez said his client would resist that.
"At the end of the day, the decision on whether to extradite Joran is political," he said.
He contends Van der Sloot could not receive a fair trial in the United States "because he's been satanized by the press. He is seen as a demon in the United States and would be judged by a jury made up of common people who are influenced by the press and would surely give him the maximum sentence."
Van der Sloot is imprisoned in the Piedras Gordas prison just north of Lima.
His attorney said he expects his client will serve at least two-thirds of his 28--year sentence before being paroled.
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Associated Press writer Jay Reeves contributed to this report from Birmingham, Alabama.
