The A Team singer introduced the couple – who got together in December – when he was living in LA last year.
Courtney Cox and Johnny McDaid
"I’m not sure that it’s public knowledge, so maybe I shouldn’t have said anything – but, yes, they’re already living together," said Ed, speaking at an exhibition opening in London.
"Things are moving fast. He moved in and, judging by the last time I saw them, they couldn’t be happier.
"They get on really well and are genuinely good friends, pardon the pun."
Courtney Cox and Ed Sheeran are really good friends
Asked if wedding bells could soon be sounding for Northern Ireland-born musician Johnny and Courtney, Ed replied: "I wouldn't be surprised, but it's still early days.
"They certainly enjoy each other's company and feel very comfortable with each other."
The romance between the actress and the Derry-born musician is clearly going well. The pair took a romantic break to Venice for Valentine's Day, and Johnny even flew in his mum and family in to meet his new girlfriend.
A source told the Daily Mirror: “Family is really important to Johnny and like most Derry boys his mammy’s blessing to the woman in his life is important.
"Introducing his mum Pauline and siblings to Courteney shows just how serious he is about her.
"Pauline’s a lovely lady and they’re a really nice family.
"They’re all very down-to-earth so their main priority is Johnny’s happiness no matter if that’s with someone who’s a celebrity or not.
"She would keep her own counsel on private matters but she says she seems nice."
Courteney and Johnny were also joined on holiday by hernine-year-old daughter Coco, from her marriage to David Arquette.