Medvedev won just over 70% of votes on Sunday, and will be inaugurated as president, replacing Vladmir Putin, on May 7.
"Bush congratulated Medvedev on his election as Russian president and stressed that he intended to continue constructive cooperation until the end of his presidential term," the spokesman said.
"Both parties expressed their intention to continue the tradition of mutual trusting, frank and open dialogue set by Putin and Bush, which has been crucial for development of Russian-American relations."
The United States will elect a new president on November 4, 2008, and Bush will leave office in January 2009.
The U.S. National Security Council spokesman issued a statement confirming Bush had spoken to Medvedev.
"President Bush told Mr. Medvedev that he looks forward to working with him and that he hopes the two can establish a close working relationship that will help them deal with important world issues," Gordon Johndroe said in a statement.