The 37-year-old star - who has previously featured in a TV series about his life following his first marriage to singer Jessica Simpson - will appear with his new wife in 'Nick and Vanessa's Dream Wedding' on TLC a few weeks after the nuptials.
The pair said in a statement: "We're lucky to have such passionate and loving fans, and we thought partnering with TLC on this special would be the best way to share the exciting Journey we're on with all the people that support us and our relationship."
In addition to the marriage itself, the show will also feature footage including Vanessa's search for her dream dress and their joint wedding shower.
Nick has previously revealed he is keen to start a family soon after getting married so he can catch up with his brother Drew, who has two children.
He said: "I'd like to be a dad sooner than later. I'm getting up there. I've gotta catch up with my brother. [Drew's] got two and I've got zero, so the pressure is on me!"
"I'm at a point in my life where I'm ready to start another chapter. Having kids is a big part of that. I'm excited for what comes next. Life is a journey, and I'm certainly ready to close this chapter and move on to the next."