Terms of the deal, which was announced Wednesday on Blink's website, are not being disclosed.
Messages sent through the Blink app self-destruct after a certain amount of time. The app allows users to send texts, sketches, record audio, make videos and take photos. Its main rival is Snapchat, which Facebook reportedly tried to buy for $3 billion.
Blink said it will shut down both the iOS and Android versions of the app in the coming weeks before the switchover.
The move comes amid both Yahoo's continued efforts to reinvent itself and rising interest from social networking companies in mobile messaging apps.
Sunnyvale, California-based Yahoo Inc. has bought numerous startups since the arrival of CEO Marissa Mayer two years ago in an attempt to increase its mobile presence and reverse a decline in advertising revenue.
Meanwhile, Facebook spent $19 billion earlier this year to buy the Mountain View, California-based messaging app WhatsApp, which had 450 million users at the time, after its attempts to buy Los Angeles-based Snapchat failed.