Sergei Ivanov, who was arrested in possession of forged documents under various different names, will be extradited to Spain within 45 days.
The suspect is accused of murdering two Germans at their Spanish villa. Ivanov's fingerprints were found at the crime scene and he also is believed to have used the victims' credit cards after the killings.
An arrest warrant was issued by Spain in 1997.
If found guilty Ivanov could face up to 25 years in prison.