The former 98 Degrees singer proposed to Minnillo last November after four years of dating.
The pair exchanged vows on Friday after sending just 35 close friends and family invites in the form of plane tickets.
The guests were then flown to a mystery location to attend the ceremony.
Lachey tells People.com, "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."
And Lachey's new bride is already planning to become a mom.
Minnillo says, "For us, this is just a stepping stone to do what we ultimately want and that's to start a family together."
It is Minnillo's first marriage; Lachey was previously wed to Jessica Simpson.