Billy and Alexis got married in a secret wedding ceremony at their Long Island home over the Fourth of July weekend, after dating since 2009.
Alexis, 33, is a former Morgan Stanley executive and equestrian.
Little Della is Billy's second child. He also has a daughter, 29-year-old singer/songwriter Alexa Ray, from his marriage to Christie Brinkley.
Following Billy and Alexis' clandestine nuptials, Brinkley congratulated the couple on Instagram, writing, "Congratulations to the glowing bride and groom.. And to my daughter Alexa, who has a wonderful friend in Alexis! Wishing the growing family every happiness!"