Chinese authorities said Google must keep its mobile software, Android, free for other device makers for up to five years.
The acquisition is Google's biggest to date.
The internet search giant has also named a new management team for the phone handset maker.
Motorola is a leading manufacturer of smartphones and other devices.
Google's takeover of the business allows it to move into the manufacturing of phones and tablet computers for the first time.
Google's chief executive, Larry Page, said in a blog post that there were people using devices now who may never use a desktop machine: "The phones in our pockets have become supercomputers that are changing the way we live. It's now possible to do things we used to think were magic, or only possible on Star Trek- like get directions right from where we are standing; watch a video on YouTube; or take a picture and share the moment instantly with friends."