Mr Burns, 41, was being considered as ambassador to the Czech Republic but that posting was not going to be available until 1998, while the Greece posting is available later this summer, officials added.
One source said that the Secretary of State, Madeleine Albright, had pushed hard for Mr Burns' appointment to Athens. She has said that the dispute between Greece and Turkey about Cyprus is among the regional problems on which she wants to focus.
Mr Burns has been State Department spokesman since January 1995. He was appointed by the then Secretary of State Warren Christopher and has been serving Ms Albright temporarily until she names a permanent spokesman, expected to be James Rubin, one of her closest aides.
Before his appointment as spokesman, Mr Burns, a career diplomat, was senior adviser at the National Security Council on Russia and other former Soviet states. As a diplomat, Burns served in Cairo and the American consulate in Jerusalem.