The ceremony took place in Hawaii in front of a small group of family and friends. According to reports, guests were asked to sign a non-disclosure agreement.
Jack's wife Stelly has now spoken to Hello magazine about the year the couple have had, including Jack's MS diagnosis and the birth of their daughter Pearl.
"We've dealt with a lifetime's worth of problems in one year," she said. "We've got through it all and I just know we'll be together forever."
Jack also said that he felt like marriage would make their bond "even stronger", explaining: "Having Pearl and now marrying Lisa are just the best things ever. They have changed my life."
Jack's mum Sharon Osbourne said that she is happy her son has found "his partner in life", and said it was lovely because the family is getting bigger. "There was just the five of us, and now we have Pearl and Lisa. We adore Lisa," she added.
The full spread of the wedding appears in this week's Hello.