The man comes from Mlada Boleslav, around 50 kilometres north-east of Prague and was recognised by his mother from photographs, Mlada Boleslav police spokesman Ladislav Mares told the Czech news agency, CTK.
The man was held in Sweden after being rescued by a Norwegian ship last month when it found him drifting on a makeshift raft of barrels and planks in international waters between Norway and Denmark.
The man, identified by Swedish police only as Jyri, speaks good English and had told Swedish authorities that he came from California. He claimed he had been thrown off a British boat.
Swedish police later said they believed he had spent the past two years homeless in Britain.
Czech police said he emigrated to Germany in 1989 and stayed abroad until 2002. Between 2002 and 2004, he lived in various parts of the Czech Republic and abroad, Mares said. The man is not wanted by Czech police, he added.
Swedish police spokesman Thomas Fuxborg earlier cited information passed on by Interpol from German authorities that the man was born in 1957 in the Czech Republic.
They were waiting for Czech authorities to confirm his identity, which can been proven by fingerprints, Fuxborg said.
Swedish police also learnt that for the past two years the man was homeless and living in the British county of Essex, where he had to report regularly to police, he added.