The Pointless host has been in a relationship with the 45-year-old actor and comedian - best known for playing Petronella Osgood in the sci fi series - since September 2021 and they are now engaged to be married.
Osman, 51, was asked by The Observer if it is true they are set to wed, to which he replied: "Yes. Exciting, isn’t it?”
The TV presenter and author of bestselling crime novel The Thursday Murder Club revealed on Desert Island Discs in 2021 that he and Oliver had begun a relationship in the summer and she had moved in with him in October that year.
He told Lauren Laverne: "[I'm] now in a place where I want to be. I'm happy with myself, I've got these beautiful kids, I've met the woman who I'm going to be with for the rest of my life.
"That thing of competition and ambition, you soon realise that rocket fuel disappears and it's about happiness and my kids bring me happiness and Ingrid brings me happiness."
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Osman was married to jazz singer Sumudu Jayatilaka up until 2007, and they share adult children Ruby and Sonny.
Oliver is one half of comedy double act Watson and Oliver with fellow stand-up Lorna Watson. They had their own BBC sketch show in 2012.
As well as appearing in Doctor Who and Silent Witness, Oliver has appeared in Hollywood movies Last Christmas and The Hustle, alongside Anne Hathaway and Rebel Wilson.
Osman recently took part in BBC show Who Do You Think You Are?, during which he discovered one of his ancestors had started an amateur detective group, just like in his best-selling book.
In his episode of the BBC show, which investigates the family tree of participating celebrities, Osman chose only to learn about the heritage of his mother's side of the family.
That is because, as he has spoken publicly about before, his father walked out on the family when he was nine-years-old.
Read more: Why is Richard Osman leaving 'Pointless'?
Osman, 51, grew up in Haywards Heath, West Sussex with his mother Brenda Wright and older brother Mat Osman, of the Britpop band Suede.
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