In a closed session, Mr Grossi received the support of 24 members of the 35-nation board of governors, ahead of Romania’s Cornel Feruță with 10 votes.
A further board meeting open to all IAEA member states will be held on Wednesday to appoint Mr Grossi, the agency said in a statement.
The board of governors’ decision will be submitted for approval to the IAEA general conference, which consists of representatives of all 171 member states.
The new director-general – appointed for a term of four years – will be the IAEA’s sixth head since it was founded in 1957. He is likely to assume office no later than 1 January 2020.
Mr Grossi succeeds Yukiya Amano of Japan, who died on 18 July 2019. Mr Amano was the agency’s fifth director-general. He was first appointed to the office effective December 2009 and reappointed in 2013 and 2017.
He followed Mohamed ElBaradei, IAEA director-general from 1997 to 2009; Hans Blix, from 1981 to 1997; Sigvard Eklund, from 1961 to 1981; and Sterling Cole, from 1957 to 1961.