The veteran diplomat, who has been serving as Argentina's ambassador to the IAEA, will be the agency's first leader from Latin America.
Grossi previously held high-level posts at the agency between 2010 and 2013, according to AFP.
Grossi will be taking over from Yukiya Amano, who died in July at the age of 72 having been in post since 2009.
While the US is thought to have lobbied in his favor, diplomats say Grossi has stressed his belief in the importance of the agency's impartiality.