This will the 55-year-oldโs fourth child in four years.
The exciting news of the birth was reported by Swedish regional newspaper, Sundsvall Tinding.
โAnna Eberstein from Sundsvall has had her second child with film star Hugh Grant,โ the paper stated.
โThe newest member of the family saw the light of day for the first time last Wednesday.โ
Anna and Hugh are already parents to their son, John, and itโs been reported that the wider family are said to be overjoyed by the birth.
The 37-year-oldโs mother, Susanne confirmed to Swedish newspaper รrnskรถldsviks Allehanda the baby, her second grandchild, had been born.
โI can confirm that I have another grandchild,โ she happily told the publication.
โIt is wonderful that we now have grandchildren [more than one grandchild].โ
While a close family friend revealed to the MailOnline that โEverything seemed to have gone okay,โ it remains unclear whether Anna gave birth in Sweden or the UK.
Earlier this year, in October, it was noted that the Swedish native was expecting for the second time, however, neither Hugh or Anna commented on the pregnancy.
Hugh hasnโt spoken out much on fatherhood, but close friend and mother to his godson, Liz Hurley admitted โhe is a good daddy, very good.โ
Including his newborn and son John, born in September 2012, Hugh also has two other children, a daughter, Tabitha, four, and Felix, two, with Chinese-born receptionist and actress Tinglan Hong.
At the time of Tabithaโs birth, Hughโs spokesman said:
โHe and the mother had a fleeting affair and while this was not planned, Hugh could not be happier or more supportive. He and the mother have discussed ยญeverything and are on friendly terms.โ
While Hugh took matters into his own hands following the birth of Felix, tweeting, โIn answer to some journos. Am thrilled my daughter now has a brother.โ
Adding, โAdore them both to an uncool degree. They have a fab mum.โ
Congratulations to Hugh and Anna, we canโt wait to meet your bundle of joy!