Erdogan said the cutting-edge opera house would give new life to Taksim Square in central Istanbul.
The 2,500-seat opera house, due to open in early 2019, will be built on the site of the Ataturk Cultural Centre (AKM) which has been unused for over a decade and whose impending demolition has worried some architects.
Erdogan said the cutting-edge opera house would give new life to Taksim Square in central Istanbul, which was the hub for mass protests against his rule in 2013 sparked by an urban development project in the nearby Gezi park.
Backers of the project want the opera house to be as much as symbol of Istanbul as the Bolshoi Theatre is in Moscow or the Sydney Opera House in Australia.
"God willing it will become an honour and symbol for Istanbul and our country," Erdogan said in a speech in Istanbul.
The AKM, which for years has stood as an empty shell on Taksim Square, has had an unfortunate history.
It opened in 1969 but then closed almost immediately after a fire. It reopened in 1978, becoming the centre of Istanbul cultural life, but was then shuttered in 2008 for restoration that never took place.
Critics of the new project complain it will remove a symbol of the modern Turkish Republic founded after the break up of the Ottoman Empire by Mustafa Kemal Ataturk, from whom the building takes its name.
But Erdogan said the resistance to the building's renewal was "not because of sensitivity to culture but ideological obsessions."
He added: "After protests, court cases and commotion, the path of science, intellect and rationality has prevailed."
Taking a swipe at the Western-educated intelligentsia who criticised the project, he added: "I know that the new AKM will benefit the most those who have sabotaged it for years."
He added Taksim -- seen by many Istanbul residents as a chaotic mess best avoided -- would be fully pedestrianised with vehicle traffic passing underground, bringing a "new richness to the square".
In a signal the government does not want to be seen trampling over the past, the architect of the new building, Murat Tabanlioglu, is the son of Hayati Tabanlioglu, the architect of the original AKM.
The glass-covered modernist facade of the new building is also similar to the old edifice.
Opera houses are usually the places where rich elites go, "but this should change. They should be places where everyone can go," said Murat Tabanlioglu.