Musicians including Dua Lipa, Chris Martin, Ellie Goulding, Anne-Marie and Rita Ora lent their voices to the BBC Radio 1 Live Lounge version of Times Like These, which went to number one in May.
Net profits from the single in the UK were split between Comic Relief and BBC Children In Need.
Producer Fraser T Smith, who has worked with Dave, Adele and Stormzy, said the involvement of Foo Fighters frontman Grohl was “the most amazing icing on a really nice cake”.
The 49-year-old Grammy award winner told the PA news agency: “We cast the net out very wide and I think the perfect people were involved for the record.
“It ended up being a very star-studded cast, but with this kind of thing it’s the meaning of the lyrics that comes through, so there is a sort of natural democracy to it all, which is where great music comes from.
“It was a great song, there were enough people who were going to sing it brilliantly.
“As it turned out, it was a star-studded cast but that wasn’t necessarily the driving force behind it.
“And of course, we didn’t expect to get Dave Grohl on the record, but he very graciously stepped in at literally the 11th hour.
“That became the most amazing icing on a really nice cake.”
Smith, who is releasing his debut solo album 12 Questions under the moniker Future Utopia, said the experience of building the song had been unnerving.
He said: “To be working with Radio 1 and the Live Lounge – this great institution – was brilliant, but it was also quite daunting to have all of these incredible artists uploading these vocals which were recorded, to be fair, from a professional way through to some artists recording on their phones.
“We had to try and make sense of what was going on from a sonic point of view, but also from an emotional point of view.
“Every artist we worked with pulled out something incredible from being locked down.”
A video for the single was broadcast during BBC One’s The Big Night In fundraiser and saw more than 20 musicians performing from their own homes.
Smith said he had aimed to treat each musician’s recording with respect, but joked he did not want the song to feel like a “Live Aid moment”, in reference to the 1985 benefit concert.
He said: “We put the email out which was, ‘If you want to bang a saucepan or record something on your phone, however you want to do it, that’s fine.
“’Don’t feel this is a Live Aid moment, as great as that was.
“’This is like everyone gathering around the virtual campfire in your own homes and putting something together, and we will treat what you send with the utmost love and respect, and make something that isn’t this fully blown polished record but is all about integrity and warmth and feeling, and this acoustic version of this great original Foo Fighters classic.’”
Described by Smith as “the most ambitious, exciting and terrifying thing I’ve ever done”, his forthcoming debut solo album sees a series of collaborations, including with Stormzy, Dave and Idris Elba, tackle 12 questions about life and humanity.
12 Questions is released on October 23.
