© ReutersA man using the name Uri Brodsky hides his face under a hood as he is escorted into a courtroom by armed police in Warsaw.
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.
'Mistaken identity'
Mr Brodsky, who was arrested by border guards at Warsaw airport last month, has three days to appeal against the decision.
However, his lawyers say no decision has yet been made. They argue it is a case of mistaken identity and he is not the man wanted in Germany.
Mr Brodsky hid his face from reporters as he walked to the courtroom escorted by anti-terrorist police officers.
He showed no reaction when the ruling was announced.
Forged passports from the UK, the Irish Republic, France, Australia, and Germany were used in the Dubai operation, leading to diplomatic rows between those countries and Israel.
The UK and Australia have expelled Israeli diplomats over the forgeries.
Dubai police have identified more than 30 suspects in the case.
Comment: Note that the Polish guards are heavily armed and have their faces covered. What does that say about the assessment of Polish authorities of the threat from Israel and it's intelligence agency?...