Johanna Sigurdardottir and writer Jonina Leosdottir were officially married on Sunday, the day the law came into force, the PM’s adviser Hrannar B Arnarsson said.
The pair had been in a registered partnership since 2002 and had applied to have it converted into a marriage under the new law. No ceremony was held.
The law was passed without a dissenting vote in Iceland’s parliament on June 11.
Social Democrat Sigurdardottir, 68, became prime minister last year after the previous centre- right government was ousted as the country’s economic crisis emerged.