The 58-year-old diplomat will replace Antonio Guterres, of Portugal, who was UN High Commissioner for Refugees since 2005, a UN statement said yesterday.
Grandi's appointment must be endorsed by the UN General Assembly, which is widely seen as a formality.
Grandi, who will take up the job on January 1, was head of the UN Palestinian refugee agency UNRWA from 2010 to 2014, after serving as its number two from 2005 to 2010. He was also deputy envoy to the UN aid mission in Afghanistan.
Guterres is due to step down at the end of the year after leading UN efforts to help 60 million people worldwide who have been driven from their homes by wars and persecution.
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UNHCR has said that number marks an all-time high, surpassing the 50 million people who were displaced during World War II.
Grandi beat out former Danish prime minister Helle Thorning-Schmidt and German Achim Steiner, the director of the UN Environment Program, for the key post.