The celebrity couples' representatives confirmed some details of the surprise destination wedding to People.com, but did not give away its exact location.
"Nobody knew where they were going," Minnillo told the celebrity news Web site.
"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," Lachey said.
Minnillo is the new host of "Wipeout."
Lachey, who is also a singer, is the emcee for "The Sing-Off."
People.com said the couple's vow-exchange was taped as the special "Nick & Vanessa's Dream Wedding," which is to air July 30 on TLC.
Lachey and his ex-wife Jessica Simpson starred together in "Newlyweds: Nick and Jessica," a reality show that ran from 2003 to 2005.