The couple said "I do" in Williams's childhood village at St Nicholas's church in Bathampton, which she had attended since the age of six.
"I was thinking about the awesome days in my life and realised a wedding day tops everything," the former skeleton racer told Hello magazine.
Williams won gold at the 2010 Winter Olympics in Canada, but announced her retirement in 2012, citing injuries as her reason.
"After two weeks together it was like, 'This is it'."
It appears the couple were destined to meet as she logged onto the app while on a train from London to Bath.
As the app uses your location to find you a match, she may not have met Ham, who is based in Hampshire, otherwise.
"I didn't know what I was doing," she said light-heartedly.
"I was an accident," added Ham.
Ham is a warrant officer class two (AQMS) with the Royal Electrical and Mechanical Engineers.
As such, he wore his ceremonial uniform during the wedding, while Williams wore an Augusta Jones dress from Krystle Brides of Bath boutique.
