Former player and coach Rafnsson defeated Turgay Demirel of Turkey, the only other candidate, with 32 of the 51 votes.
“I am very moved by the support which was even more than I expected,” said Rafnsson. “Being FIBA Europe president is a huge responsibility and the hard work starts now.
“The people you have here are magnificent. The passion and enthusiasm of the people working for our federations. If we don’t exploit this then we are making a mistake.”
Rafnsson served as a member of the FIBA Europe Board from 2006 to 2010. He is also president of the National Olympic Committee of Iceland. He will serve a four-year term as FIBA Europe president running from 2010 to 2014.