"During the call, the two leaders discussed a range of issues including the threats and challenges facing the United States and Russia, strategic economic issues and the historical U.S.-Russia relationship that dates back over 200 years," the Trump transition team said in a statement.
The Russians said in a statement that Putin congratulated Trump, and pledged to build "dialogue with the new administration on the principles of equality, mutual respect and non-interference in the internal affairs of each other."
The U.S. and Russian leaders also agreed to set up a face-to-face meeting soon.
The two men "agreed to assess the current very poor state of Russian-American relations" and to work for "constructive cooperation on a wide range of issues."
Democratic candidate Hillary Clinton criticized Trump over his praise of Putin during the campaign. She and other Trump critics pointed to a U.S. intelligence assessment that Russian interests were behind the hackings of US Democrat Party members and may have tried to influence the elections.
Putin denied the allegations. Trump also expressed skepticism, and said the United States should seek better relations with Putin and Russia.
The Russians said that Putin and Trump "agreed to continue contacts on the phone and in the future to provide for a personal meeting."
The Trump team said that he "noted to President Putin that he is very much looking forward to having a strong and enduring relationship with Russia and the people of Russia."