"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 following the vote.
Iraqi Kurdistan includes the three northern provinces of Sulaimaniyah, 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 an historic day that all Kurds should celebrate."
Barzani heads the Kurdistan Democratic Party (KDP), one of two main parties in the region along with the Patriotic Union of Kurdistan (PUK).
A giant portrait of Mustafa Barzani overlooked the assembly, flanked by Kurdish flags representing the territory he had claimed for Kurds in the middle of the 20th century before Saddam Hussein's Baath party came to power.
The swearing-in ceremony that was scheduled for Sunday was postponed two days owing to a weather conditions, as a sandstorm swept across Iraq.
The younger Barzani was chosen to lead the Kurdish provinces following four months of talks with the PUK, which is led by his former rival and current Iraqi President Jalal Talabani.
Both parties took pains to make the day one that would live on in Kurdish history books.
Following the 1991 Gulf War, the two parties fell out over power-sharing and tax revenues in the region and thousands died in ensuing fighting, with Barzani even calling in Saddam's forces to fight the PUK on his behalf.
The two sides then formed an alliance following the Iraqi dictator's fall in April 2003, agreeing to defend their right to autonomy within a federal Iraq.
January 30 national elections left the Kurds as the second strongest political force, after Iraqi Shiites, but it took the KDP and PUK four months to reach agreement on who would hold the regional presidency, a decision that saw their parliament finally open on June 4.
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.