The Four Weddings and a Funeral Actor, 51, had a short relationship with Tinglan Hong, 32, who is understood to be an actress.
Hong gave birth on September 26 at the private Portland Hospital in Central London. On the day of the birth, Grant was at the Labour Party conference in Liverpool.
However, he is said to have spent 30 minutes with his daughter the next day, before heading to Scotland to play golf.
Though the pair are no longer a couple, a spokesman for Grant said last night: “I can confirm that Hugh Grant is the delighted father of a baby girl. He and the mother had a fleeting affair and while this was not planned, Hugh could not be happier or more supportive.”
The spokesman added: “He and the mother have discussed everything and are on very friendly terms.”
However, the statement did not disclose the identity of the mother.
Grant and Hong began dating in January, but it is said that the relationship fizzled out soon after she became pregnant.
Though Grant has enjoyed a string of high profile relationships, most notably with Elizabeth Hurley and Jemima Khan, he has never married.
Four years ago the actor told Vogue magazine: “As much as I adore myself, I’m quite keen to find someone else to care about more. I remember reading a Warren Beatty quote when he finally had children and said what a relief it was not to be all me, me, me.”