The 7-inch tablet, manufactured by Asus, is gradually making its way into shops, with some warning of shipping delays of up to two weeks.
British buyers have yet to be told when they will be able to get their hands on the device, although retailers expect supplies this week.
The Nexus 7 is the first Android tablet to come with Jelly Bean, the latest version of Google’s mobile operating system.
Aggressively priced from £160, it is designed to loosen Apple’s grip on the tablet market; Android tablets from third party manufacturers such as Samsung and Motorola have so far failed to make much impact. Google's attempt is being compared to Amazon's Kindle Fire, which is only available to American buyers.
In the United States, major retailers including GameStop, Sam’s Club and Staples are already reporting shortages of the Nexus 7.
Google unveiled its first own-brand tablet, at its I/O developer conference last month.
Reviews of the Nexus 7 have been largely positive, with many impressed by the build quality and features given the relatively low price. It has an Nvidia Tegra 3 quad-core processor, and a 1.2-megapixel camera, and will be available with 8 or 16GB of storage.
Apple is expected to respond to the threat from Android tablets with a smaller, cheaper iPad later this year.
