Councillors voted by seven to three on Wednesday in favour of the £75 million venue, which will be created between St Andrew Square and the new St James Quarter.
It is hoped the complex, first announced in 2016, will be open to the public from 2026 on a site currently occupied by empty offices.
The biggest new cultural venture in Edinburgh since the Usher Hall in 1914, the Dunard Centre is being funded by American arts philanthropist Carol Grigor, the UK and Scottish governments and the city council.
It will be suitable for classical, pop, rock, jazz, world music and electronica concerts, as well as spoken word events.
The venue, which is being created on a site effectively donated to the project by RBS, will create a new home for the Scottish Chamber Orchestra (SCO) and the Edinburgh International Festival concerts.
The green light was welcomed by a host of leading acts from Edinburgh’s music scene, including The Proclaimers, Anna Meredith and Idlewild.
EIF director Fergus Linehan said: “This decision is fantastic news for the city and for music in Scotland.
“Edinburgh is a city famous for its cultural life and home to world-renowned arts festivals, which generate more than £300 million for the economy, but it lags behind many other cities in its provision of cultural infrastructure which currently deters some artists from choosing to perform in the city.
“By creating a modern hall with outstanding facilities and acoustics, we are closing the recognised gap in the region’s cultural infrastructure and helping to sustain Edinburgh’s position as a leading cultural city against national and international competition.
“At the same time, we are creating a year-round cultural hub to offer a diverse range of performances and an extensive education and community outreach programme.”
SCO chief executive Gavin Reid said: “The approval is tremendous news for the city and turns the ambition for a world-class centre for music and performance into a reality.
"The Dunard Centre will become our new home and will be transformational.
"A stunning auditorium offering the very best in modern acoustics and boasting state of the art digital broadcast facilities will allow us to dream big, expand our repertoire, collaborate with ever more composers and artists, and present our work innovatively, courageously and flexibly, all with a new-found sense of adventure and ambition, always seeking to reach more and more people.”
Idlewild frontman Roddy Woomble said: “Since I’ve known the city, many great venues have come and gone, but the Dunard Centre sounds like it will be here to stay – an ambitious, creative space that will encourage and showcase local talent, alongside national and international performers.
“New music is always going somewhere in Edinburgh and the Dunard centre will see that it gets there.”
The Proclaimers (Craig and Charlie Reid) said: “The Dunard Centre will be a prestigious and fantastic cultural asset to the city.”
Anna Meredith, one of Scotland’s leading composers and musicians, said: "As someone who works across creative genres, this kind of space is especially exciting to me as it offers the flexibility to allow artists to work across mediums and realise their work to its full potential.”