They hope to initially help third-party contact-tracing apps run efficiently.
But ultimately, they aim to do away with the need to download dedicated apps, to encourage the practice.
The two companies believe their approach - designed to keep users, whose participation would be voluntary, anonymous - addresses privacy concerns.
Their contact-tracing method would work by using a smartphone's Bluetooth signals to determine to whom the owner had recently been in proximity for long enough to have established contagion a risk.
If one of those people later tested positive for the Covid-19 virus, a warning would be sent to the original handset owner.
No GPS location data or personal information would be recorded.
"Privacy, transparency and consent are of utmost importance in this effort and we look forward to building this functionality in consultation with interested stakeholders," Apple and Google said in a joint statement.
"We will openly publish information about our work for others to analyse."
President Trump said his administration needed time to consider the development.
"It's very interesting, but a lot of people worry about it in terms of a person's freedom," he said during a White House press conference.
"We're going to take... a very strong look at it, and we'll let you know pretty soon."
The European Union's Data Protection Supervisor sounded more positive, saying: "The initiative will require further assessment, however, after a quick look it seems to tick the right boxes as regards user choice, data protection by design and pan-European interoperability."
But others have noted that the success of the venture may depend on getting enough people tested.