(Translated by https://www.hiragana.jp/)
Apple - iTunes - The App Store has reached 10 billion downloads
The Wayback Machine - https://web.archive.org/web/20110927201449/http://www.apple.com/itunes/10-billion-app-countdown/

Thank you. Ten billion times. The App Store has reached 10 billion downloads. Thanks for getting us there.

Contest Winner

The 10 billionth app, Paper Glider, was downloaded by Gail Davis of Orpington, Kent, in the UK. As the grand prize winner of Apple's 10 Billion Apps Countdown promotion, Gail will receive an iTunes Gift Card worth US$10,000.
View the official rules

10 Billionth Download

Paper Glider
View in the App Store