Terms of the deal, announced Monday, weren't disclosed.
The move shows Microsoft remains eager to win share in education, where Google's Chromebooks have become popular.
Microsoft is making Flipgrid free of charge. Schools that already have subscriptions will receive prorated refunds, Microsoft said.
The acquisition comes one and a half years after Microsoft announced a partnership with Flipgrid. Today, Flipgrid integrates with many Microsoft products, including Teams for chatting with other people and OneNote for taking notes. But Flipgrid has paid to use Amazon Web Services cloud, which competes with Microsoft's own Azure.
In the U.S., nearly 60 percent of all mobile personal computing devices that were shipped to K-12 schools in the fourth quarter were Chromebooks, while less than 26 percent used Windows, according to Futuresource.
Microsoft sought to strengthen its education strategy with the release last year of a Surface Laptop and Windows 10 S, which is limited to running apps downloaded through Microsoft's app store to deliver sufficient performance and security.
Hardware is just part of Microsoft's challenge at schools, though.
Google introduced Google Classroom in 2014 as a place for teachers to give out assignments and for students to hand them in, using the company's productivity apps like Google Docs. In 2016, Microsoft unveiled a similar tool called Microsoft Classroom as part of its Office 365 productivity software package for education. It has since retired that product and added assignment features to Teams.
But Flipgrid on its own is much more focused on video than Teams, with more than 20 million users. And it will retain its brand, rather than get pushed into Teams, Microsoft says.
The start-up was founded in 2015 and headquartered in Minneapolis, with 24 employees listed on LinkedIn. Competitors include Recap and Seesaw.