The couple, who tied the knot in a private island ceremony last month, broadcast the ceremony in a TLC special Nick and Vanessa's Dream Wedding.
"Just the two of us. [We] opened a bottle of wine and plopped down on the couch and watched it Saturday night," Lachey told Access Hollywood of tuning in for the event.
"It was pretty cool. There were things I didn't even remember happening. It was kind of neat to sit down and kind of relive it."
Lachey added that he was glad to do the special as it serves as "the best wedding video you could have" and will be a nice keepsake to show his and Minnillo's future children.
Minnillo recently revealed that she and Lachey wrote their own wedding vows to make them "more personal".
Lachey has said that the pair are currently enjoying the routine of married life.