Miller said the opportunity to take the 9-month-old boy to the competition in Sochi is "such a unique, once-in-a-lifetime experience," the New York Post reported Monday.
As a Family Court referee looked on, Miller handed over the boy to his ex-girlfriend, Sara McKenna. The child was the product of a brief relationship between the pair last year in California.
McKenna had lost custody after a California court ruled a month ago she shouldn't have left the state while she was pregnant. A New York court reversed the ruling.
McKenna, 27, is a student at Columbia University.
The infant is named Samuel Bode Miller McKenna, but Miller calls him Nathaniel.