The Team GB pair, who boast 10 Olympic golds between them, tied the knot on Saturday.
Announcing the news, Kenny, 28, tweeted a snap of his new wife in bed saying, "Good morning Mrs Kenny."
Trott's father added: "So pleased to announce that my darling daughter @LauraTrott31 married @JasonKenny107 yesterday."
Kenny's image of his new wife pictured her in bed with their two dogs, Sprolo and Pringle, at her feet.
She posted on Instagram: "The happiest day of my life. With all my family and close friends I married my best friend."
"We had the most amazing day and I'm so pleased to finally be able [to] call Jason my Husband".
The pair, who live in a cottage just outside Knutsford, Cheshire, turned down an offer to have the wedding featured in a magazine and managed to keep the details a secret from the press until it had happened.
Mrs Kenny's father tweeted his congratulations with two pictures of the happy couple outside St Alban & St Paul Church in Macclesfield.
The bride's sister Emma, who was maid of honour at the ceremony, tweeted a picture of Mrs Kenny in her dress and said: "Couldn't have asked for a better day for my baby sister. #TrottKennyWedding".
Friend and fellow cyclist Dani King, who won gold with the 24-year-old in the women's team pursuit at London 2012, was among the bridesmaids.
She retweeted a photograph from the father-of-the-bride, adding: "And what a day it was too", next to a red love heart and the hashtag #mrandmrskenny.
Another teammate from Trott's world record-breaking team which won pursuit gold at Rio 2016, Joanna Rowsell Shand, said the images were "beautiful photos".
The couple asked guests to donate to Dementia UK.
The reception was held at the Hilltop Country House, near Prestbury Village in Cheshire.
In a Facebook post, the venue said: "While the whole country was talking about the Bake Off tent, Laura Trott &Jason Kenny were sharing their first dance in ours."
Laura, whose hometown is Cheshunt in Hertfordshire, is a four-time Olympic champion after retaining the team pursuit and women's omnium titles in Rio that she won at London 2012.
Jason has seven Olympic track sprint medals to his name - including six golds - making him the holder of the most titles for a Briton alongside former team-mate Sir Chris Hoy.
The relationship between the pair began during the build-up to the London 2012 Olympic Games.
Trott has said "it wasn't love at first sight" when she first met Kenny, who she said never spoke to her in training.
Kenny said in response that he "never said hello to anyone" and he could not help being "grumpy".
Kenny's mother Lorraine has said the first time she "knew something was happening between the two of them was when Jason phoned me up and said, 'I'm bringing Trotty home for a bacon butty.'"
"We liked her from the off," she said.
The Bolton cyclist popped the question while sitting on the sofa watching an episode of EastEnders in 2014.
Cycling's golden couple, Laura Trott and Jason Kenny, have got married in a private ceremony in Cheshire.