Tomasdottir led her rivals with 34.3 percent of the vote, followed by former prime minister Katrín Jakobsdottir, who came second with 25.2 percent, according to official figures.
Jakobsdottir had reportedly congratulated Tomasdottir when she spoke to the RUV during her election party.
The president's role is largely ceremonial in Iceland, although he or she has the power to veto laws and to call a referendum in certain situations.