The disco-tinged song – the second single from Gaga’s new album Chromatica – secured 8.1 million streaming plays in seven days.
It is also Gaga’s first single to debut at number one in the UK, according to the Official Charts Company.
The track notched up a total of 70,000 chart sales, taking the crown from last week’s leader, DaBaby’s Rockstar featuring Roddy Ricch.
Gaga told OfficialCharts.com: “If someone told me the day I wrote Rain On Me, a day I was crying water like misery, that this song would someday be number one, I never would have believed them.
“Thank you for celebrating this song. It’s my gift to you, to celebrate yourself. I hope the whole world is dancing.
“To all my UK monsters, I love you so much from the bottom of my heart. Thank you for making me number one, and I hope you feel number one every time you listen to this song.”
Both Gaga and Grande now have six UK number one singles each, joining the likes of Queen, Britney Spears and Sir Rod Stewart.
Rain On Me is also the first all-female collaboration to hit number one in six years, since Grande teamed up with Jessie J and Nicki Minaj on Bang Bang in 2014.
Rockstar fell to number two, while Rover by S1mba featuring DTG was at number three, and Say So by Doja Cat was at number four.
Death Bed by Powfu featuring Beabadoobee was at number five.
Think About Things by Icelandic singer Daoi Freyr, Iceland’s Eurovision entry for the cancelled 2020 contest, climbed nine places to number 34 after becoming a viral hit on TikTok.
On the albums chart, The 1975 claimed their fourth consecutive number one, with Notes On A Conditional Form scoring 34,000 chart sales.
Physical sales made up 71% of that figure, including 7,000 copies on vinyl, making it the fastest-selling album on vinyl of 2020 so far.
The 80s-indebted synth-pop group held off YouTuber and rapper KSI, who took number two with his debut solo album Dissimulation, with 27,000 chart sales this week, 70% of which came from streams.
With reporting by Press Association