John Ausonius, a Swedish citizen born to a German mother and a Swiss father, was handed over to German police in January, after they decided to revive the 25-year-old case.
Ausonius got into a quarrel with the victim, Blanka Zmigrod, on a visit to Germany, accusing her of stealing from him while he was visiting the restaurant where she worked. A week later, she was shot dead.
"The prosecutor deems that there is sufficient evidence, partly from witnesses and partly from the bullet cases found at the scene of the crime, which match completely with those collected as evidence in Sweden," Nadja Nielsen from the Frankfurt prosecutor's office told TT newswire.
Nielsen said that the trial would hopefully begin in the summer.
Ausonius denied carrying out the murder when questioned at the time and still maintains his innocence.
Ausonius was sentenced to life imprisonment in 1994 for shooting eleven people between 1991 and 1992, almost all of whom were immigrants.
One, Iranian student Jimmy Ranjbar, died of his wounds.
He was dubbed "The Laser Man" by Swedish press because of the laser sights he used on the rifle with which he is believed to have shot his first victims. He later switched to a revolver.
Ausonius has become one of Sweden's most well-known serial killers, in part because of the bestselling book about the case by the Swedish journalist Gellert Tamas.