It was claimed last week that the comedian was dating the Take That singer after impersonating him in the Fake That music video for Comic Relief in March.
Fellow comedian John Bishop, who also starred in the spoof, has revealed that Tate was the one to pursue a date with Orange.
Speaking on The Graham Norton Show on BBC One, he said: "Catherine looked like Jason and said to him, 'We should have a coffee, can I get your number?'. And he said, 'Yeah'.
"It must be odd fancying someone that looks like you! Good luck to them, they're both lovely."
The new couple have subsequently been on several dates to the theatre and the cinema.
A friend said: "It's a very unlikely pairing but they have really hit it off. They've been on a number of dates. They really enjoy each other's company."
Tate will return to The Office later this year to reprise her role as Nellie Bertram, NBC announced on Friday.
Watch Catherine Tate perform as part of Fake That below: