The deal, which has been thrashed out in the last week, will see the government and council contribute Â£5 million each over the next five years.
Organisers of the city’s main festivals have also pledged to try to raise a further Â£5 million through commercial sponsorship and private donations under the three-way agreement.
The deal has been agreed two years after a major study into the future of the festivals called for action to be to taken to ensure Edinburgh retained its place as the “undisputed world leader as a festival city.”
The Thundering Hooves study, which was described a “spur to action” for the city and the country, warned that the festivals risked losing their “premier division status” unless their funding was maintained in the face of growing overseas competition.
The city’s year-round festivals are currently worth around Â£313 million to the city’s economy - a figure which has risen by almost a quarter in the space of five years. Events like the Edinburgh International Festival, the Fringe, the Tattoo and the Hogmanay festival now attract a record 4.5 million people each year – up by more than 250,000 in the same period.
However the festivals have been making a case for extra funding due to a 15 per cent “real terms” drop in support over the last five years, due to soaring transport, licensing, policing and traffic management costs.
The new funding, designed to "protect the legacy and strengthen the future" of the festivals is aimed at boosting their global reputation by creating new international links, targeting major new markets for both audiences and artists, and extending the main tourism season by creating new spring and winter events.
Other key elements include getting more Edinburgh-based artists involved with the festivals and their international partners, taking more festival events to “disadvantaged” parts of the city and encouraging more Scots to take in the festivals for the first time.
First Minister Nicola Sturgeon is expected to confirm the Scottish Government’s backing for the deal this weekend as the city’s flagship events draw to a close after what is expected to be another record-breaking season.
A deal was brokered between the council and the government after earlier hopes that the festivals could benefit from the Â£1.1 City Region Deal were dashed, although it did include a new Â£20 million concert hall.
Council leader Adam McVey said: “We will be taking forward a tri-party fund to support the festivals in the next five years. That will be enormously beneficial in securing what is the most vibrant environment on the entire planet.
“The world descends on us in August. We’re under pressure to sustain that, but we also have a responsibility to continue it and make sure it remains a vibrant element of this city’s future.
“Our festivals have been driving Edinburgh’s tourism industry for 70 years. If we’re to sustain our position as the world’s festival city and protect their legacy, we need to make a joint commitment towards supporting their future success.
"In this crucial year, we need to recognise how our festivals support tourism, create jobs and develop the creative and hospitality industries.
“It seems to have been an absolutely bumper years in terms of people going to see shows and visiting shows. It’s an indication of the calibre of artists who are coming to the city to be part of this fantastic experience.”
Scottish culture secretary Fiona Hyslop said: "The internationally renowned Edinburgh festivals attract visitors from across the world every year and make a significant contribution to our economy.
"We have long made clear our commitment to supporting the festivals - awarding Â£19 million since 2008 through the Edinburgh Festivals Expo Fund."
Julia Amour, director of Festivals Edinburgh, which works with 11 of the city's most high-profile year-round events, said: "We are committed to working with both the city council and the Scottish Government to capitalise on our enormous value for the benefit of everyone in Edinburgh and Scotland."