They reportedly began dating just under a month ago, after Grande split from her boyfriend of two years, the rapper Mac Miller, and Davidson broke up with his girlfriend Cazzie David.
Since then they have posted plenty of affectionate messages and videos on Instagram and Twitter, and went to Kanye West's album listening party for Ye together last week.
Reports of their engagement emerged after they attended a house party hosted by Robert Pattinson where they reportedly told guests they were getting married; after which Grande appeared to confirm the rumours on her social media accounts.
Responding to a fan who tweeted: "I hope he knows he is marrying us as well," she tweeted: "HAHAHAHAHAHAHA HE'S BEEN BRIEFED."
The 24-year-old also told her friend, fellow pop star Camila Cabello - who often calls her "wife" - that they "need to talk".
Davidson recently got two tattoos for Grande: her initials on his finger; and the bunny ears logo she is associated with, on back of his neck.
Davidson joined the cast of SNL aged 20 in 2014, making him one of the youngest actors ever to be on the show. He has also appeared on the popular sitcom Brooklyn Nine-Nine, and had a cameo in the Amy Schumer cameo Trainwreck.
The Independent has contacted a representative of Grande for comment.
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