BERLIN — The European Commission settled its antitrust case against Apple and four book publishing groups over e-book price fixing Thursday, in what was called a victory for the leading online seller, Amazon.com, and a setback for publishers.

The investigation ended after Apple, Simon & Schuster, HarperCollins, Hachette, and Holtzbrinck agreed to end their attempt to set prices for e-books. Under agreements made in 2010, publishers could set prices, with the retailer acting as an agent taking a commission. Apple championed this model.