About 99 percent of the shares that voted at a special meeting favored the deal. That represents about 74 percent of Motorola Mobility's outstanding shares as of Oct. 11, the company said.
The board had already accepted the offer when it was announced in August. The deal is expected to close early next year, although it must still be approved by government regulators.
The U.S. Justice Department is in the midst of an extended review of the deal.
Motorola Mobility Holdings Inc. is one half of the old Motorola Inc., which split up in January. The other half is Motorola Solutions Inc., which makes police radios, bar-code scanners and other equipment for government and corporate clients.
Motorola Mobility shares were unchanged at $38.94 on Thursday.
Google shares added 13 cents to $601 in aftermarket trading after slipping $10.60, or 1.7 percent, to $600.87 in the regular session.
Source: News Wire and AP