Bernt Olov Lnge Eriksson, 67, would be sent back to Sweden while Christopher Pierre Verdino, 28, would be extradited to France, said Immigration Chief Major General Chidnupong Yuktatad.
He was speaking at a media conference at Phuket Immigration headquarters in Phuket City, with French suspect Mr Verdino presented to journalists.
The Frenchman alleged raped a disabled waitress in France, Immigration officers said, before fleeing to Thailand on October 30.
He was tracked to a Patong restaurant where he was working as a chef and arrested there yesterday by Phuket Immigration Chief Colonel Sanya Chokkayaikid.
Mr Eriksson was also arrested in Patong by Colonel Sanya as he went for a stroll along beach road on January 14.
Both men had overstayed their visas and may face penalties in Thailand before being extradited.