The App Store currently offers more than 425,000 apps for iOS devices, including games, business, news, education, sports, travel and health.
Apple said that it has sold in excess of 200 million iOS devices since the launch of the first iPhone, meaning there has been around 75 downloads for each iPhone, iPod Touch and iPad sold.
Philip Schiller, Apple's senior vice president of worldwide product marketing, said: "In just three years, the revolutionary App Store has grown to become the most exciting and successful software marketplace the world has ever seen.
"Thank you to all of our amazing developers who have filled it with over 425,000 of the coolest apps and to our over 200 million iOS users for surpassing 15 billion downloads."
Nicholas Callaway, chief executive of developer Callaway Digital Arts, said: "We're bringing Martha Stewart, Angelina Ballerina, Sesame Street and many more of the world's most popular books and magazines to iPad.
"We knew the iPad was going to be a revolutionary storytelling device, but never could have anticipated it would become so popular, so quickly."
Mark Rein, vice president and co-founder of Gears of War studio Epic Games, added: "iPad provides us with an unparalleled mobile device for creating gorgeous, immersive games. Infinity Blade has been a runaway hit with customers around the world and we couldn't be more excited about our success on iOS devices."
Google said at its I/O developers conference in May that the Android Market had topped 4.5bn downloads, with 100m Android devices generating around 500m downloads each month.
In January, Microsoft lobbied US authorities to reject a bid by Apple to trademark the words 'App Store', arguing that the term is far too generic.