This will the 55-year-old's fourth child in four years.
The exciting news of the birth was reported by Swedish regional newspaper, Sundsvall Tinding.
"Anna Eberstein from Sundsvall has had her second child with film star Hugh Grant," the paper stated.
"The newest member of the family saw the light of day for the first time last Wednesday."
Anna and Hugh are already parents to their son, John, and it's been reported that the wider family are said to be overjoyed by the birth.
The 37-year-old's mother, Susanne confirmed to Swedish newspaper Örnsköldsviks Allehanda the baby, her second grandchild, had been born.
"I can confirm that I have another grandchild," she happily told the publication.
"It is wonderful that we now have grandchildren [more than one grandchild]."
While a close family friend revealed to the MailOnline that "Everything seemed to have gone okay," 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 hasn't spoken out much on fatherhood, but close friend and mother to his godson, Liz Hurley admitted "he is a good daddy, very good."
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 Tabitha's birth, Hugh's spokesman said:
"He 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 everything and are on friendly terms."
While Hugh took matters into his own hands following the birth of Felix, tweeting, "In answer to some journos. Am thrilled my daughter now has a brother."
Adding, "Adore them both to an uncool degree. They have a fab mum."
Congratulations to Hugh and Anna, we can't wait to meet your bundle of joy!