The founders of Mojang, the main beneficiaries of the deal, also announced their departure from the company.
"Mojang is being bought by Microsoft," the Swedish company confirmed after a week of media speculation about the takeover.
Minecraft is one of the world's most popular videogames -- often described as digital Lego, where players fight to survive in a hostile world populated by monsters while having the power to re-design the environment as they progress.
Despite far less sophisticated graphics than many successful competitors, the game has succeeded in seducing both children and more seasoned video gamers.
Since its release in 2009, over 50 million copies have been sold for a range of platforms including Microsoft Xbox, PlayStation Sony, PCs, tablets and smartphones, ensuring enormous wealth for its creators.
Microsoft is already an established player in the videogame business with its Xbox console although its latest version (Xbox One) has fared less well than PlayStation 4, released at the same time last year.
However the acquisition of Minecraft is expected to boost the company's rating with gaming enthusiasts.
"The founders: Notch, Carl, and Jakob are leaving. We don't know what they're planning," wrote the Swedish company on its website, adding that "the vast majority (if not all) Mojangstas will continue to work at Mojang for the time being.