A joint statement said the boards of both companies had unanimously approved the deal, which should be completed by the end of this year, or early in 2012.
Earlier this year, Motorola split into two separate companies.
Mobility develops and manufactures mobile phones, while Motorola Solutions covers wider technologies for corporate customers and governments.
The deal would allow Google to “supercharge” its Android operating system, the joint statement added.
Google said it would continue to run Mobility as a separate business.