Users of the Android mobile operating system have downloaded 10 billion apps as the Android Market is averaging 1 billion downloads a month since July, Google (GOOG) announced Tuesday.

Android’s growth has accelerated exponentially in the last year: Mountain View-based Google’s operating system ran more than half the smartphones sold in the third quarter of 2011, according to research firm Gartner, double its market share from the previous quarter.

In the same period, Apple’s (AAPL) share of the mobile market dropped from 17 percent to 15 percent, according to Gartner, but the quarter ended just before the newest iPhone running the Cupertino company’s iOS mobile operating system was released. Apple said 4 million iPhone 4S devices were sold just in the opening weekend.

Apple surpassed 15 billion app downloads in July, the same month Android surpassed 6 billion downloads; since then, Google has averaged 1 billion app downloads a month, Android developer Eric Chu said in a blog post announcing the milestone.

To celebrate the achievement, Google has partnered with app developers to offer a selection of apps for 10 cents apiece for the next 10 days; Tuesday’s offerings include the popular mobile game Minecraft.

Contact Jeremy C. Owens at 408-920-5876; follow him at Twitter.com/mercbizbreak.