Mr Gambari is a former Nigerian foreign minister who is currently serving as UN special envoy to Burma.
He will take up his post on 1 January
Mr Gambari replaces Congolese diplomat Rodolphe Adada, who stepped down earlier this year.
Levels of violence have fallen in the region in recent months.
Violence flared in Darfur in 2003 when black African rebel groups took up arms against the Sudanese government in Khartoum, complaining of discrimination and neglect.
Pro-government Arab militias then started a campaign of violence, targeting the black African population.
The UN says some 300,000 people have been killed in the six-year conflict. Khartoum says about 10,000 have died.
Source: BBC News