The company has confirmed it is no longer backing the event, less than a year after it was targeted by environmental campaigners.
Festival organisers say the relationship with BP came to a “natural end” last year, but insisted it was the company’s decision to end its backing.
The festival urged to ditch BP, a long-time supporter of the EIF, amid claims it was being allowed to “greenwash” the event, which listed the company as a “festival partner.”
The festival, which has refused to state how much its backing from BP was worth, has been one of a number of leading British arts organisations which has come under pressure over their links with BP over the company’s environmental record.
It emerged last month that the Tate had ended its own sponsorship deal with, 100 around prominent figures from the arts, science and politics urged the British Museum to end its backing at the weekend.
Theatre-maker Simon McBurney, one of the biggest names in last year’s EIF programme, was among those to join protesters outside the Usher Hall when they staged a demonstration featuring drama and song.
He said at the time: “The EIF just doesn’t need BP’s sponsorship. It makes BP look good by accepting their money. It is deeply troubling.”
The remaining official partners of the EIF include Edinburgh-based technology incubator Codebase, financial services firm Ballie Gifford, van rental firm Arnold Clark, and the city’s Sheraton Grand and Waldorf Astoria hotels.
Festival director festival Fergus Linehan said: “The BP sponsorship of the festival has just ended. It was definitely their decision. It was nothing to do with any protests last year. That was not the reason.
“Their sponsorship sort of come to an end last year, after a very long time. You don’t have to be a rocket scientist to work out that BP is in a different place from where it used to be.
“It hasn’t had a particular big impact on us. We have had a really great year generally in terms of funding, we’ve had really good support in particular from donors and foundations.”
Amanda Grimm, spokeswoman for the campaign group BP or not BP Scotland, said: “We are delighted that the sponsorship deal between BP and the Edinburgh International Festival has not been renewed.
“The world is shifting away from fossil fuels, and we believe that arts and cultural institutions, as trend-setters and forward-thinkers, should be at the forefront of this vital shift.”
Ric Lander, finance campaigner with Friends of the Earth Scotland, said: “We need to urgently move away from extracting and burning fossil fuels and companies like BP who continue to profit from the destruction of our environment have no place in our treasured cultural events or institutions.”
A spokeswoman for BP said: “In what is an extremely challenging business environment, we are reducing spending and taking many difficult decisions across BP.
“We are delighted to have supported the Edinburgh International Festival for a number of years however, as a result of the current business environment, we have reluctantly decided not to renew our sponsorship this year.”