"Catherine and Jeff have known each other for years,' said a source. 'Jeff is a screenwriter, so he and Catherine have been working on several writing projects together. He's a funny, good-looking guy but it's been hard for his ex-wife to deal with the fact that he is dating someone so famous."
Mr Gutheim, 52, is considerably less well-known than his fiancee. His work includes a 2005 teen comedy called Full Of It, which starred Baywatch actress Carmen Electra, and a 2009 comedy called Knucklehead, starring wrestler Big Show.
The romance is believed to have begun after Mr Gutheim split from his British-born wife of 19 years, Tracey. The couple have three children, aged 20, 16 and 14.
Ms Tate moved to America in 2011 when she landed a role in the US version of The Office, but maintains a London home.
"Catherine is known in the US but she's not the household name there that she is in Britain," said the source. "That's why she and Jeff have been able to keep their relationship under the radar.
"It's not like they have been hiding. They've been quite open about their relationship and have been talking openly about getting married. They are very much in love and blissfully happy. They can't wait to start this next chapter of their lives together."
The pair are said to be planning to split their time between Hollywood and Britain once they are married.
Ms Tate shot to fame with her BBC2 sketch show in 2004, and has gone on to earn a reported £5 million fortune thanks to her gift for both comedy and serious acting.
Last night, she finished a sell-out West End run of a stage version of her comedy show featuring popular characters such as foul-mouthed pensioner 'Nan' and surly teenage Lauren Cooper.
Ms Tate has also performed with the Royal Shakespeare Company and at the National Theatre, while she famously played Donna Noble opposite David Tennant in Doctor Who.
She first appeared in the show's 2006 Christmas special entitled The Runaway Bride before becoming the Doctor's regular companion for the fourth series in 2008. She last appeared in the show for a 2010 Christmas edition.
She is also the voice of Magica De Spell in Disney's animated series DuckTales.