But it is believed there are still major problems with both versions of the technology in calculating distances between devices, casting doubt on whether the electronic contact tracing scheme will ever be implemented.
Announcing the move, NHS test and trace boss Dido Harding, and Matthew Gould, who leads the NHSX team, said the decision had been made after they identified "specific technical challenges".
"Our response to this virus has and will continue to be as part of an international effort," they said.
"That is why as part of a collaborative approach we have agreed to share our own innovative work on estimating distance between app users with Google and Apple, work that we hope will benefit others, while using their solution to address some of the specific technical challenges identified through our rigorous testing."
Speaking at the daily Downing Street briefing, Mr Hancock said he would leave "no stone unturned" in developing a working system.
"Over the past few weeks we have rigorously tested our prototype app in the Isle of Wight and in field trials," he said.
"Because of this testing, we discovered a technical barrier that every other country building their own app is also now hitting.
"We have found that our app works well on Android devices, but Apple software prevents iphones being used effectively for contact tracing unless you’re using Apple’s own technology."
And Mr Hancock said the Government had agreed to "join forces" with the tech giants to develop the new system, adding: "We’ll share our algorithm and the work that we have done on distance calculation and combine that with their work.
"Coming together in this way will bring together some of the best minds to find a solution to this global challenge and help to save lives.
"In the meantime the NHS test and trace system based on good old fashioned human contact tracing is working well, identifying local outbreaks and helping to control this virus."
The Health Secretary had initially earmarked a late May launch for the Government-backed app, which was intended to play a key role in the national “test and trace” strategy to combat Covid-19.
The Cabinet minister said at the time that the public had a "duty" to download the application — currently being trialled on the Isle of Wight — to their devices when it becomes available.
Responding to the news, shadow health secretary Jonathan Ashworth ministers should now "urgently prioritise" the development of a working test and trace system.
“This is unsurprising and yet another example of where the government’s response has been slow and badly managed. It’s meant precious time and money wasted.
“For months tech experts warned ministers about the flaws in their app which is why we wrote to Matt Hancock encouraging the government to consider digital alternatives back in May.
“Ministers must now urgently prioritise building a fully effective test, trace and isolate regime lead by local expertise to break the chains of transmission of this deadly virus.”
Meanwhile, Lib Dem acting leader Ed Davey, said: "The Government have been told for months their app wouldn’t work but the ploughed on regardless, acting like they knew best.
"These delays could have cost lives. We need an urgent independent inquiry into the Government’s handling of this pandemic."
And Jim Killock, executive director of the Open Rights Group, said there were still concerns about the accuracy of the technology.
"People need to trust the app, and it needs to work. Some countries using decentralised matching have already released their apps," he said.
"It will also work across borders. Decentralised matching makes the app much easier to trust, as it doesn’t track you.
"We are still worried that employers and others may try to force people to use the app. A safeguards bill could help by making this unlawful."
He added: "There are also still significant questions about whether Bluetooth matching is sufficiently accurate, and whether the government will do enough to make people feel they should follow any advice to get a test or isolate."