user: The council would invest £1m each year for a period of five years - with match funding from the Scottish government and Edinburgh's Festivals.
One of the aims of the fund is to extend the tourism season in winter and late spring.
Council leader Adam McVey said the plan would protect Edinburgh's position as "the world's festival city".
Mr McVey said: "Our festivals have been driving Edinburgh's tourism for 70 years. Attracting audiences of over 4.5 million every year, they add £313m to the Scottish economy.
"If we are 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."
The aims of the fund, which marks the 70th anniversary of the International Festival, include:
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.
"The Scottish government has long made clear our commitment to supporting the festivals - awarding £19m since 2008 through the Expo Fund.
"I welcome the council's in-principle agreement to invest an additional £5m over the next five years and we are finalising our discussions on the Scottish government's support for the festivals."

Sum: The City of Edinburgh Council has proposed a new fund to protect the legacy of the city's festivals.


Article: In a scathing report, John Sopko said that officials bought "forest" pattern uniforms, despite the country's landscape being only 2.1% wooded.
The decision was "not based on an evaluation of its appropriateness for the Afghan environment", he wrote.
A former Afghan defence minister chose the pattern in 2007, he says.
In the 17-page report, Mr Sopko writes that Minister Abdul Rahim Wardak chose the privately owned pattern over a cheaper pattern that the US military already owned.
US officials, who had been searching for patterns online with Mr Wardak, authorised the purchase because he "liked what he saw", they wrote at the time.
"My concern is what if the minister of defence liked purple, or liked pink?" Mr Sopko told USA Today in an interview.
"Are we going to buy pink uniforms for soldiers and not ask questions? That's insane. This is just simply stupid on its face.
"We wasted $28 million of taxpayers' money in the name of fashion, because the defence minister thought that that pattern was pretty."
For years, Mr Sopko's office has criticised the Pentagon for wastefulness during the United States' longest war.
In January, he told a think tank in Washington there was evidence that Taliban leaders had instructed commanders to purchase US fuel, ammunition and weapons from Afghan soldiers, because it is cheaper.
Senator Chuck Grassley called the uniform decision "embarrassing and an affront to US taxpayers".
"Those who wasted money on the wrong camouflage uniforms seem to have lost sight of their common sense," the Republican senator added.
The Pentagon is currently considering raising the level of US troops in Afghanistan, with a formal announcement expected this week.
++++++++++
Summarize:

assistant: US taxpayers unnecessarily spent $28m on uniforms for the Afghan National Army, according to the US inspector general tasked with overseeing the war.