The couple welcomed their first child, daughter Harper Renn Smith, on Tuesday in Los Angeles, her rep tells PEOPLE exclusively.
Baby Harper, who weighed in at 8 lbs., 3 oz., is "doing great," as are the new parents.
Thiessen's colleagues say motherhood is something the actress is more than prepared for. "She's totally the den mother of the show," White Collar costar Matt Bomer told PEOPLE in February. "She's so organized and so loving and generous – that can only make her an absolutely amazing mom."
Added costar Tim DeKay: "She'll make a great mom."
Thiessen, 36, and Smith, an artist and actor, who have been married since 2005, have said that starting a family is "something we've wanted for a long time and we are thrilled that it's actually happening."
Reporting by JULIE JORDAN