Eliasson, who currently serves as Swedish ambassador to the United States, will replace Jean Ping, of Gabon.
The Swedish diplomat will take the presidency as the world body will adopt deep reforms proposed by Secretary General Kofi Annan.
“The essence of the reform project of the UN is: building a UN which effectively and legitimately responds to the urgent needs around the world,” Eliasson said in a speech following his election.
“Today, multilateralism is being put to the test. We must live up to the demands that development, security and human rights put before us.”
Sweden and Gabon will share the chairmanship of the UN’s summit in mid-September, which the heads of government of the organisation’s 191 member states are expected to attend.
Eliasson was the Swedish ambassador to the United Nations from 1988-1992, during which time he was the secretary general’s personal representative to Iran and Iraq.
He was the president of the UN Economic and Social Council (ECOSOC) in 1990-1991 before serving as under secretary for humanitarian affairs.