Motorola Mobility, which separated from the rest of Motorola earlier this year, manufactures phones that run Google's Android operating system.
This is Google's biggest acquisition to date. The move means /*Google*/ could compete more directly with /*Apple*/.
Google will pay $40.00 per share, a 63 percent premium to Motorola's closing price on Friday.
The acquisition has the approval of both companies' boards and is expected to close by the end of this year or early 2012.
The Associated Press contributed to this report.