The couple, who got engaged last year, tied the knot in a ceremony on a tropical island - with just 35 of their closest family and friends in attendance.
"For us, this is just a stepping stone to do what we ultimately want and that's to start a family together," Minnillo told People.
The pair kept the location of the event a surprise for guests. "Nobody knew where they were going," she said.
Lachey added: "Our wedding invitations were in the form of a plane ticket. We told them they were going away and the attire was 'island chic.' It was all very vague."
Minnillo wore a two-piece Monique Lhuillier ensemble, while Lachey opted for a Dolce & Gabbana suit.
The wedding will be televised in a TLC special called Nick & Vanessa's Dream Wedding, which premieres July 30 from 9-11pm ET/PT.
> Nick Lachey, Vanessa Minnillo 'were unsure of TV wedding'