The pair collaborated on a remix of Lipa’s song Levitating alongside Madonna.
Lipa told Apple Music that she had been a longtime fan of the US hip hop star.
She added that when they discussed the collaboration Elliott told her she felt “inspired” by the remix, adding: “I want to jump on it.”
Lipa said: “I jumped on the phone with her and we had a little talk and she really just does stuff that she really believes in, so that I felt it was such a massive compliment for me, to be so inspired by the remix and the track, and to want to be a part of this mixtape.
“And it really is a dream come true.”
She added that Madonna is an artist she has listened to throughout her life.
“I guess her career trajectory as well has been something so inspirational and the momentum that she’s kept and the way that she’s grown with her music,” Lipa said.
“And I’ve always found that really, really inspiring.”
The song features on Club Future Nostalgia The Remix Album, which features reworks of songs from Lipa’s album Future Nostalgia, which was released earlier this year.