The pop star attended the wedding, which took place on May 25, with his American actress girlfriend Danielle Campbell. Contrary to reports, he did not perform on the day.
Vardy, 29, and his wife, 34, tied the knot at Peckforton Castle in Cheshire.
The bride wore a Caroline Castigliano gown. The couple's 19-month-old daughter Sofia was a flower girl.
Vardy told Hello! that seeing his bride and daughter walk down the aisle made him emotional.
"I'd been holding it together so well until that point, but when I saw Sofia's little face as she was walking down towards me, I felt myself starting to go," he said.
"Then I saw Becky coming towards me and she just looked so incredible, I felt my composure going again.
"I knew she'd look amazing, but it was more than I could ever have pictured," he said.
Mrs Vardy spoke with warmth about her husband's qualities.
"I'm so proud of him and of what he's achieved, but most of all, I'm proud of the man he is," she said.
"He's the most brilliant father and partner and I know he is going to be the best husband I could wish for."
She continued: "He's not one for grand romantic gestures, but I don't need that. He shows his love in the ways that matter, by being there for me and the kids and making me feel loved."
Wedding guests included rapper Tinchy Stryder, Leicester City fan Sergio Pizzorno of rock band Kasabian and Vardy's Leicester City team-mates, who were still celebrating their incredible Premier League win.
Tomlinson also said playing Vardy in a biopic about the former non-league striker's rise to fame would be a "golden opportunity".
The One Direction star, who was a guest at the Leicester City and England player's wedding to Rebekah Nicholson, is set to play Vardy in a biopic.
"It's a golden opportunity," Tomlinson, 24, told Hello! magazine when asked about the planned film. "Jamie's story is incredible - he's incredible."
The singer and Doncaster Rovers fan added: "He's a lovely guy, very easy-going and such a great example for anyone who thinks they can't follow their dreams."
Leicester City, who faced relegation last season, won the Premier League title in what has been described as one of the greatest sporting stories of all time.
Tomlinson added: "For a football fan, any kind of involvement in a story like Jamie's is exciting."