Google Inc. wants Android to be the operating system for virtual reality.

In the wake of Facebook Inc. ’s $2 billion purchase of Oculus VR, Google has assembled a team of engineers to build a version of the Android operating system to power virtual-reality applications, according to two people familiar with the project.

Those people said Google has “tens of engineers” and other staff working on the project. Google plans to freely distribute the new operating system, they said, mimicking a strategy that has made Android by far the most popular operating system for smartphones, powering more than one billion phones. A version of Android for smartwatches has been less successful so far, with devices using it registering few sales.

A Google spokeswoman declined to comment.

The project is speculative, because no virtual-reality devices are yet shipping in large numbers. But game companies, filmmakers and others see huge promise in the field.

Virtual reality was the highlight of this month’s Game Developers Conference in San Francisco. Attendees waited for two hours for a demonstration of the Oculus product, and there were similarly long lines to see virtual-reality technology from chip makerNvidia Corp. Many other booths had VR headsets for people to test out new games.

Facebook jumped ahead of rivals by buying Oculus, which makes a headset that wearers strap over their eyes to project virtual-reality images. Facebook Chief Executive Mark Zuckerberg has said that virtual reality will be the next “computing platform” after mobile devices, and he hopes Oculus will power a new generation of “immersive” experiences, from games to remote learning to virtual doctor appointments.

The Oculus deal helped spark a race to develop virtual-reality systems. Samsung Electronics Co. , the largest maker of Android smartphones, has joined with Oculus for its Gear VR headset. Sony Corp. has developed its own headset called Project Morpheus.Microsoft Corp. is working a device called “HoloLens” that projects images onto real-world settings, as are many startups.

Punctuating its rivalry with Google, Facebook last month poached a high-profile executive from Google’s advanced-projects lab, Mary Lou Jepsen, to work on Oculus. Her background is in display technology.

Oculus uses its own hardware and software for its headset, just as Apple Inc. uses its own hardware and software for the iPhone. Software developers build their applications on top of these systems.

Android is an “open” operating system available free to hardware makers. There are now four versions of Android, for smartphones, wearable devices, televisions and cars.

For its part, Google last year was the lead investor in a $542 million round of funding for Magic Leap Inc., a Florida-based startup that is developing its own eyeglasses-like device designed to project computer-generated images over a real-life setting. Separately, Google has another team testing a special tablet that uses multiple cameras to “augment reality” by projecting images onto real world objects.

The team working on Android for virtual reality is led by Clay Bavor and Jeremy Doig. Mr. Bavor’s LinkedIn describes him as a vice president of product management and Mr. Doig’s as a director of engineering. Mr. Bavor helped create the company’s low-tech virtual-reality viewer called “Google Cardboard.”

Unveiled last summer, it is a piece of cardboard with two magnets, two lenses, a rubber band and some Velcro, which fold into a crude virtual-reality viewing tool. Users place smartphones into the viewer, which render images in 3-D. The Cardboard app for Android smartphones has been downloaded more than one million times since last summer.