He was a "deeply committed internationalist who fought throughout his life for a fairer and more peaceful world", the statement added.
Mr Guterres led the tributes to his predecessor. "In many ways, Kofi Annan was the United Nations. He rose through the ranks to lead the organisation into the new millennium with matchless dignity and determination," he said in a statement.
UN high commissioner for human rights Zeid Ra'ad Al Hussein said in a tweet he was grief-stricken over Annan's death: