He will quit his current post as an Australian member of parliament to take up the job as the special envoy of Ban Ki Moon, the UN secretary-general.
In an interview with The Australian newspaper on Tuesday, Downer pointed to his experience as a diplomat in some of the world's major hotspots, but admitted that the job of uniting Turkish and Greek Cypriots was "not going to be a cakewalk".
"These things are always untidy. It's never easy to do. We ended the civil war in Bougainville [in Papua New Guinea]. We played our part in Iraq and Afghanistan. Why not try to fix up Cyprus as well," he was quoted as saying.
Kevin Rudd, the Australian prime minister, said he had discussed the move during a conversation with the UN secretary-general late on Monday.
"We believe this is an important role for the United Nations, and we are completely behind Mr Downer's appointment," Rudd said.
Cyprus was split in 1974 when Turkish forces invaded the island in response to a coup by Athens-backed supporters of union with Greece.
Talks on reunification talks have been deadlocked since 2004, when Greek Cypriots rejected a UN reunification blueprint in a referendum.
The plan was accepted by Turkish Cypriots.