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Downer, 56, was Australia's longest-serving foreign minister during more than a decade of rule by former Prime Minister John Howard's conservative government.
Howard lost his place in parliament at elections last November that installed Labor Prime Minister Kevin Rudd. Downer decided not to take a leadership post in the opposition.
Downer was expected to make a public statement Thursday when he returns to Australia from a visit to the United States and London, his office said Tuesday.
Prime Minister Kevin Rudd said he discussed Downer's appointment during a conversation with U.N. Secretary General Ban Ki-moon late Monday.
"We believe this is an important role for the United Nations, and we are completely behind Mr. Downers appointment," Rudd told reporters Tuesday.
Downer told an Australian journalist in London he was taking the Cyprus post.
"Ill be working toward helping the Cyprus saga, working as an envoy to try and resolve that long-standing issue," Downer was quoted as saying in Herald Sun newspaper.
The Australian newspaper reported in May that Ban was keen to use Downer to resuscitate stalled diplomatic efforts to reunify the island.
Downer has had his differences with the United Nations, including over Australia's military participation in the U.S. and British-led invasion of Iraq in 2003 without U.N. approval. Howard sent 2,000 troops to join the invasion.
Downer earned praise as foreign minister for helping forge a peace accord between Papua New Guinea and its restive island province of Bougainville in 1997.
He also pioneered a more interventionist Australian foreign policy in the South Pacific, such as Australia's leading role in a multinational military and police force that entered the Solomon Islands in 2003 to restore peace and public order after years of ethnic violence.