The city’s licensing board decided by six votes to two that the current requirement that music must be “inaudible” in neighbouring properties should be dropped.
Instead, the policy on noise will say that amplified music should not be an “audible nuisance” in neighbouring homes.
Labour councillor Norma Austin Hart, convener of the Music is Audible working group, welcomed the change as “a fairer and more balanced licensing policy for a city like Edinburgh”.
She said the new policy would give venues more confidence to put on live concerts.
And she said it was wrong to assume the decision would mean music being played more loudly. She said: “The current policy is failing because it is unenforceable. This will give residents a clearer set of criteria.”
Promoters, bands and venue managers had argued the current restrictions made Edinburgh one of the hardest cities in the world in which to stage events.
And all but 25 of the 526 people who responded to an official consultation supported the relaxation.
But community groups and the police said a change of policy would lead to a surge in complaints.
The Music is Audible campaign was set up two years ago in an effort to address long-standing complaints about the impact of the rules.
But councillors put off a decision on the change last month so they could hold a full hearing on the proposed and allow community groups and others to have their say.
The New Town and Broughton community council claimed residents often felt they lived “under siege” from an ever-increasing number of pubs, restaurants and leisure facilities and ever-extending hours of operation.
Southside Community Council said there was no confidence in the present system and claimed enforcement was not effective when noise problems arose. And the Grassmarket Residents Association argued the right of residents to a peaceful night’s sleep should take precedence over a desire to encourage tourists.
But supporters of the change said out of around 11,000 complaints made to the city council each year, 213 related to entertainment noise from licensed premises and just 64 of these involved live music at 18 venues.
Green councillor Chas Booth, who voted for the change, said: “The representatives from the music community made a strong case that the current noise condition is having a negative impact on music and musicians in the city.”
But he said he was disappointed the board had not accepted his proposals which would have spelled out in more detail what constituted a nuisance, promised strong action when a nuisance was established and ensured a review of the policy after 18 months.
Six community councils and a range of other organisations including Scottish Licensed Trade Association presented their views at the meeting of the licensing board.