Publicist Carrie Gordon says Grant "is the delighted father of a baby girl."
She said Tuesday that Grant and the mother "had a fleeting affair and while this was not planned, Hugh could not be happier or more supportive."
She said the pair were on "very friendly terms."
The 51-year-old star of "Four Weddings and a Funeral" and "Notting Hill" previously had relationships with model-actress Elizabeth Hurley and socialite-turned-campaigner Jemima Khan.