The 30-year-old actress took to her social media account to share a photo with the caption; 'CherubDreamin.'
It has still not been confirmed what the couple have named their first child or whether they welcomed a son or a daughter, but reports have suggested a boy.
It was six weeks ago that speculation began about the birth as celebrity friends left congratulatory comments and well wishes for the new parents on Jaime's snaps.
Fashion designer and family friend Pam Hogg said; 'It's a boy!!! Congratulations my beautiful friends!!!'
Another friend commented: 'Congratulation my beautiful, can't wait to meet your baby boy.'
The Made In Dagenham star and her boyfriend James Suckling revealed they were expecting their first child together back in September 2015.
Jaime and boyfriend James
Jaime made no secret of her desire to have a son and her happiness at finding out she was going to become a mother last year.
She told Hello! magazine she had never been happier since finding out; 'I really feel this is the next chapter for me and I've never been happier.'
Revealing she wanted children for a long time, Jaime added; 'Growing up, I always had a strong feeling that I wanted to be a mother. Whichever way my life went, I guess I felt that a role as a mummy was going to be my main calling in life.'
Jaime is the daughter of cockney 'hard man' Ray Winstone, who has appeared in film classics such as Quadrophenia, The Departed and Sweeney Todd.
'Mum and dad are ecstatic. After the news had sunk in, they were the first people I called. When I told them they were going to be grandparents, they both burst into tears. It was so cute.
'Dad can't wait to meet his grandchild. It's a beautiful time for us as a family and it's brought us even closer than we already were.'
The new mum previously dated Alfie Allen, who is the younger brother of singer Lily Allen and plays Theon Greyjoy in the HBO series Game of Thrones.
Jaime's career started when she left school to appear in cult film Kidulthood and popular E4 series Dead Set.
She has also made TV drama debuts in ITV programs Foyle's War and Agatha Christie's Poirot.