The couple, who announced in March that they were expecting a baby, confirmed to People that their son Camden John Lachey was born on Wednesday (September 12).
"We are incredibly proud to announce the birth of our beautiful baby boy, Camden John Lachey," the duo said.
"Born today at 6.54pm, he came into this world at 8lbs, 9oz and 21 inches. Love has truly been redefined for both of us."
Vanessa Lachey, who previously admitted that she always imagined having a son as her first child, announced in June that the couple were expecting a boy.
Meanwhile, Nick Lachey recently revealed how "excited" he was about becoming a father, saying: "For someone who has wanted a family for such a long time, I've looked forward to this moment. Now that it's almost here, it's awesome."