According to The Sun, the comedienne split from stage manager Twig Clark - with whom she has one daughter - before beginning to enjoy secret dates with Orange since the summer.
The pair met when Tate joined fellow comedians to play Fake That for Comic Relief in March. She took on the role of Orange, with Alan Carr as Mark Owen, James Corden as Gary Barlow, Josh Bishop as Robbie Williams and David Walliams as Howard Donald.
Having hit it off, Tate and Orange have reportedly been on a number of dates, including an overnight visit to watch the Royal Shakespeare Company perform A Midsummer Night's Dream. They have also apparently been seen arriving separately for lunch together.
"They were trying to keep things secret but looked very loved up and happy together," one onlooker told the paper, while a friend added: "It's a very unlikely pairing but they have really hit it off.
"They've been on a number of dates to the theatre and the cinema. They really enjoy each other's company. Catherine deserves someone nice and she has landed on her feet with Jason. But they have both been desperate to keep their romance secret."
Their secret dates are said to have included a visit to the National Theatre, while they also supported David Walliams during his charity swim last month.
Meanwhile, another source claimed to have seen Orange leave the former Doctor Who star's South West London home on a Sunday morning.
Representatives for Tate declined to comment on the claims, telling Digital Spy that they did not discuss "personal" stories.
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Watch Catherine Tate perform as part of Fake That below: