Ms Woodward, now 35, is believed to have given birth to a girl at the Royal Shrewsbury Hospital on New Year's Day.
The law graduate and husband Antony Elkes, a businessman, are reported to have named their daughter Holly.
She has set up a new life in a village near Bridgnorth with her husband Elkes. She runs her own dance school teaching classes at Morville Village Hall.
Ms Woodward was convicted of the second-degree murder of eight-month-old Matthew Eappen in his home in Boston, Massachusetts in 1997. But she served just 279 days after winning an appeal to reduce her conviction to one of involuntary manslaughter. The case made headlines on both sides of the Atlantic and saw the nanny thrust into the spotlight as television cameras captured her every move during the trial.
Matthew had been in Louise's care when he fell unconscious and was rushed to hospital, where he died five days later from fatal brain injuries
It was claimed in court that Louise had shaken Matthew violently and hit his head against a hard surface such as the bathroom floor. Her defence asserted that Matthew's death had been caused by an old injury sustained weeks before.
Ms Woodward was unavailable for comment today, but she and Mr Elkes, 34, are said to be "thrilled" by the birth. It is understood that both mother and child were transferred to a maternity unit near Woodward's home.
Ms Woodward has previously spoken of how she fell in love "at first sight" with her husband Mr Elkes – who runs a truck sales and hire business – at a nightclub in Chester in 2006.
She said: "We would love to have a family. We both want that. I know that it is all very quick, but it just feels right for both of us.
"Of course, I know that there are some people out there just waiting for me to have a baby so they can say nasty things. That upsets me, but that is not going to stop me leading my life. I am innocent, I have done nothing wrong. I am entitled to enjoy my life, I am not going to apologise for being happy."