The former Pointless co-host, 52, shared an image with 45-year-old Oliver in a white wedding gown and pearls taken on Saturday, holding hands and smiling.
A number of famous faces commented on the tweet, including DJ and broadcaster Lauren Laverne, actress Dawn French, TV presenter Rylan Clark and journalist Victoria Derbyshire.
Osman wrote: “The most magical, joyful day on Saturday with my beautiful wife @ingridoliver100.
“Surrounded by wonderful friends and family, a day full of love and laughter. We’re so, so happy.”
The couple first met on the set of Osman’s BBC Two gameshow House Of Games where a group of celebrities compete against each other in a series of quick-paced guessing games.
In November, Oliver tweeted a picture from her appearance on House Of Games Champion Of Champions, where previous winners return to become the ultimate champion of the show that was aired on the BBC for the first time in September 2017.
She wrote: “Last time I was on the show, I won a fiance.”
Oliver played Petronella Osgood in Doctor Who between 2013 and 2015, and also featured in the 50th anniversary special Day Of The Doctor.
She is one half of the comedy duo Watson and Oliver and also had roles in Peep Show and Silent Witness.
Osman announced in April this year that he was stepping back from Pointless after nearly 13 years on the BBC show, having co-hosted alongside Alexander Armstrong, since it began in 2009.
He said he was leaving to focus on his writing, with his debut novel, The Thursday Murder Club, published in September 2020.
It became a bestseller, with its global film rights later snapped up by Steven Spielberg’s production company Amblin Entertainment.
A sequel, The Man Who Died Twice, was published in September last year, with the third of the four Thursday Murder Club books, The Bullet That Missed, released earlier this year.