Minecraft, which has sold over 54 million copies, allows players to build structures with retro Lego-style blocks, as well as explore a large map and battle others.
The deal was announced by Xbox chief Phil Spencer.
Mojang, whose three founders will leave the company, assured fans that “everything is going to be OK”.
Some analysts have speculated the deal is designed to attract more users to Microsoft’s Windows Phone devices.
The acquisition comes a year after Microsoft bought the Finnish mobile phone company Nokia.
Minecraft is one of the top-selling apps on both Apple’s iOS store and Android’s Google Play, and has recently been released for the Xbox One and PlayStation 4, further boosting sales.
Last month, it was the third most popular console game, according to market research firm NPD Group, despite being on sale for a while.
Mojang which was founded in 2009, brought in over $100 million in profit in 2013, and employs about 40 people.
Microsoft said the Mojang team would join its game studio, which is responsible for titles such as Halo, Forza and Fable.
The tech giant’s chief executive, Satya Nadella, said: “Minecraft is more than a great game franchise – it is an open world platform, driven by a vibrant community we care deeply about, and rich with new opportunities for that community and for Microsoft.”
Mojang’s founder, Markus “Notch” Persson, has previously criticized Microsoft, and commented to Reuters that the market for Windows phones was “tiny” and not worth developing apps for.
Minecraft has a large and enthusiastic cult following, many of whom have reacted angrily to what they see as a corporate takeover of a communally-spirited independent company.
Others expressed concerns about whether fans would be able to exhibit their skills.
However, some enthusiasts made the point that Microsoft could devote larger resources to upgrading and expanding the game.
In a statement, Microsoft said it would maintain Minecraft across all its existing platforms, with a “commitment to nurture and grow it long into the future”.
Microsoft added that the acquisition was expected to be concluded by the end of 2014.
In an announcement confirming the deal on its website, Mojang reassured gamers, saying: “Please remember that the future of Minecraft and you – the community – are extremely important to everyone involved. If you take one thing away from this post, let it be that.”
Last month, Amazon bought Twitch, a site which allows users to watch other people play video games, for $970 million.
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