Swift playfully captioned the screen grab saying: "Never not rhyming with @teddysphotos".
The pair are such close friends that Ed has been publicly giving his approval to Swift's new beau, Calvin Harris.
"He's a really nice guy. Really, really nice guy,' he said, of the DJ, while speaking with ZM Online backstage at his show in Auckland, New Zealand.
When asked how he felt about Swift's new beau, Sheeran immediately assured the show's hosts that his friend was in good company.
"No, he's cool. He's a really nice guy, yeah, really, really nice guy," the performer continued of Harris.
He concluded that he'd give the seal of approval, because: "There are certain people that are just nice people in the industry."
"I met him maybe a year ago," he continued, once again adding that Swift's new man was a "really, really good guy."
One of the hosts then asked how Harris got so hot, to which Sheeran jokingly responded: "I think people blossom, so I'm still waiting."
Swift and Harris have been romantically linked since attending the BRIT Awards in February, and rumours have continued to grow as they were later spotted on several dates in March.
1989 LETS GO!
Met Monday is here!
Met'n it up with mum
Happy Birthday Rory from the best caddy in the world!
O2 success!
Fancy Seeing you here!
I'm in me mum car!
When the queen leaves...
- Daily Mail, nzherald.co.nz