Flutter vo-founder Navneet Dalal announced the deal on Flutter's website.
"Today, we are thrilled to announce that we will be continuing our research at Google," the statement read."We're excited to add their rocket fuel to our journey."
Flutter said it would continue to support its current app.
Gesture-recognition technology is widely used in gaming consoles and smart TVs. Samsung recently introduced gesture recognition for its Galaxy S4 smartphone.
The acquisition has caused speculation that Google will integrate the technology, used by some of its rivals, into its ranges of Chromebook laptops and Nexus handheld devices.
Google has not released any details of the deal.