A source told the The Sun: ‘Anna is being supported by Hugh all the way. She lives in a very comfortable property in West London and knows that Hugh is there for her. ‘
They continued: ‘Anna’s parents in Sweden know all about the relationship and she has their blessing.’
The birth comes just months after Hugh became a father for the second time to son Felix with Chinese actress Tinglan Hong.
She is also mother to Hugh's first child, a daughter named Tabitha who was born in 2011.
The Notting Hill star appeared to confirm the news on his Twitter, writing: ‘In answer to some journos. Am thrilled my daughter now has a brother. Adore them both to an uncool degree. They have a fab mum.’
He then added: ‘And to be crystal clear. I am the Daddy.’
Hugh has famously dated actress Liz Hurley and socialite Jemima Khan but is believed to currently be on the market, despite his ‘new dad’ status.