The palace says the daughter was born late Thursday.
Royal spokesman Svante Lindqvist said Friday that both mother and baby, whose name was not disclosed, "are in good health."
Madeleine, daughter of King Carl XVI Gustaf and Queen Silvia, and O'Neill wed in June in Stockholm.
The younger sister of Crown Princess Victoria, Madeleine is fourth in line to the Swedish throne.
Sweden has a constitutional monarchy in which the royals primarily serve as figureheads. The king is the country's head of state, but his powers are limited to ceremonial duties.