The move is a victory for Amazon which wanted to sell e-books cheaper than its rivals.
A spokesman at the EU insisted that its investigation was not yet finished, but Reuters insisted that it was done and dusted. An official announcement is expected next month.
It looks like the EU accepted a deal from Apple and the publishers to let retailers set prices or discounts for a period of two years, and also to suspend "most-favoured nation" contracts for five years.
The clauses had prevented Simon & Schuster, HarperCollins, Lagardere SCA's Hachette Livre and Macmillan, from making deals with rival retailers to sell e-books more cheaper than Jobs' Mob.
But the agreements stopped Amazon and other retailers from undercutting Apple's charges and the European Commission decided to investigate.
The Penguin group, which is also under investigation, did not take part in the offer, and might be the reason that the investigation has not formally closed yet.
The EU antitrust authority asked for feedback from rivals and consumers about the proposal, has not asked for more concessions.
Apple had a lot to lose. It could have faced a fine of up to 10 percent of their global sales, which in Apple's case could mean $15.6 billion.
The US Department of Justice is also investigating ebook prices. HarperCollins, Simon & Schuster and Hachette have settled, but Apple, Penguin and Macmillan have not.
The DOJ settlement required that retailers must at least break even selling all ebooks from a publisher's available list.
There was a hope that EU regulators will include a similar requirement, which would prohibit Amazon from pricing all ebooks at a loss.
In the United States, Amazon has been pricing popular titles at a loss and trying to make up the difference on a publisher's other ebooks.