Police arrested Norbert Feher on Friday in a rural area of Teruel province in the northeastern region of Aragon, where the slaying of two police officers and a rancher happened a day earlier.
During questioning by a judge, the 36-year-old said he had been in Spain since September and agreed to be sent back to Italy, the Superior Court of Justice of Aragon said in a statement.
The court said Italy could ask for him to be temporarily returned so he could stand trial for homicide and robberies before serving a possible prison sentence in Spain for the triple murder.
The Spanish judge took the testimony of Feher, who Italian media said was nicknamed "Igor the Russian", to comply with a European arrest warrant Italy had issued for him.
Spanish police said he was in possession of three firearms at the time of his arrest, two belonging to the slain officers.