Chief executive Larry Page said in a Google blog post that the deal had been completed and that he sees the unit producing "the next generation of mobile devices that will improve lives for years to come."
The completion follows approval by Chinese, US and European regulators.
Conditions from China's Ministry of Commerce included Google keeping its Android software for gadgets such as smartphones and tablet computers free and open for at least five years.
Regulators in the US and elsewhere have stressed that they will be watching to make sure that the Mountain View, California-based company does not use its acquisition of Motorola Mobility to obtain unfair advantage in the market.
Google will acquire 17,000 patents with the purchase of Motorola Mobility and has been strengthening its patent portfolio as the fight for dominance in the booming smartphone and tablet market increasingly involves lawsuits claiming infringement of patented technology.
Apple and South Korea's Samsung, whose devices are powered by Google's Android software, are currently involved in lengthy and costly patent fights being waged on several continents.
In announcing the Motorola Mobility acquisition in August, Page said it will "enable us to better protect Android from anti-competitive threats from Microsoft, Apple and other companies."
Motorola Mobility was created in 2011 when US-based Motorola Inc. split the company into a mobile devices unit and a government and public safety division known as Motorola Solutions.