The 111-member Kurdish parliament in Arbil, 350km north of Baghdad, met on Sunday as the city's streets were awash in the green, white and red flags of Kurdistan, emblazoned with a yellow sun.
"The choice of Barzani as regional president crowns hundreds of years of struggle, strewn with the bodies of martyrs," parliament Speaker Adnan al-Mufti said after the vote.
Iraqi Kurdistan includes the three northern provinces of Sulaimaniya, Arbil and Dohuk.
"I congratulate the Kurds and the families of peshmergas (guerrilla fighters) as one of their own becomes president of Kurdistan to work for their rights and defend their interests," Deputy Speaker Kamal Karkukli said.
"It is a historic day that all Kurds should celebrate."
A celebration of the appointment was postponed until Tuesday because of bad weather, which prevented many senior Iraqi and foreign officials from attending.
Barzani leads the Kurdistan Democratic Party (KDP), one of two main parties in the region along with the Patriotic Union of Kurdistan (PUK).
Kurdish parliament members
clap during Sunday's session
Barzani was chosen to lead the Kurdish provinces after four months of talks with the PUK, which is led by his former rival, Iraqi President Jalal Talabani.
On Saturday, Barzani obtained all 42 votes of his own party, as well as the PUK's 42 ballots and the remaining 27 spread among smaller Kurdish groups.
In a separate development, four Kurds suspected of belonging to Ansar al-Sunna group have been arrested at a mosque north of the Iraqi city of Kirkuk.
Kurdish security forces said on Sunday the men were suspected of being responsible for the attack that took place a week ago in Arafa neighbourhood, which targeted a convoy carrying foreign contractors.