Uri Brodsky is suspected of helping to forge a German passport used in connection with the murder of a Hamas operative in Dubai.
Mr Brodsky, an Israeli citizen, was detained in Poland in June on an arrest warrant issued by Germany.
Mahmoud al-Mabhouh, one of the founders of Hamas's military wing, was found dead in a Dubai hotel on 20 January.
Dubai police have said they are 99% sure that members of the Israeli intelligence agency Mossad were involved, although Israel says there is no proof.
"The court has decided to hand over Uri Brodsky to German authorities for judicial procedures there," Judge Tomasz Talkiewicz said, following the closed hearing at Warsaw regional court.
"The court did not decide whether Brodsky committed the crime for which he is under investigation, the court only checked whether the extradition request fulfils the formal requirements and whether the suspect is correctly identified," he added.More...