Israel appoints new Mossad spy chief
Barnea, 56, who served as a combat soldier in the elite Sayeret Matkal commando unit, joined Mossad in 1996.
He served from 2019 as the deputy head, according to Netanyahu's office.
In a ceremony marking the new appointment, Netanyahu hinted at steps Israel could take to thwart Iran from obtaining nuclear weapons.
Global powers have been meeting in Vienna since early April in a bid to bring Washington back to the 2015 nuclear deal with Tehran, which the US left in 2018.
The withdrawal under then president Donald Trump and re-imposition of sanctions led to Iran stepping up its nuclear activities.
Israel opposes the deal.
"There could be a situation in which our highest goal -- to guarantee that the Ayatollahs don't stop the 2,000-year existence of the Jewish people -- will require us to take brave and independent decisions," Netanyahu said, in remarks distributed by his office.
Iran maintains its nuclear programme is peaceful.
Barnea will replace Yossi Cohen, who has led the agency since 2015.
Cohen played a prominent role in recent deals to normalise ties with Arab countries. He travelled to the United Arab Emirates and Bahrain, as the US brokered deals between them and Israel.
He also reportedly joined Netanyahu on a 2020 visit to Saudi Arabia, for talks with Crown Prince Mohammed Bin Salman. Saudi Arabia denies the meeting occurred.
Cohen was linked to Israel's killing last year of Iranian nuclear scientist Mohsen Fakhrizadeh, although Israel has not commented on the incident.
Barnea's appointment was expected.
In December, Netanyahu announced that he had chosen a person identified as "D" as a replacement for Cohen, but required approval by a committee for top civil service posts.