Close friends say the 35-year-old and her husband Antony Elkes, 32, are "thrilled".
The 35-year-old was jailed in America for killing a baby in her care 16 years ago.
The English law graduate was found guilty of shaking Matthew Eappen to death 10 weeks after she got a job as a nanny, aged 19, for Boston-based Debbie and Sunny Eappen.
Although Woodward was originally jailed for 15 years, she was released after 279 days when she won an appeal to reduce her conviction to involuntary manslaughter.
Speaking about his decision, the judge at the time said: “The circumstances in which the defendant acted were characterised by confusion, inexperience, frustration, immaturity and some anger, but not malice in the legal sense supporting a conviction for second-degree murder.”
Upon hearing that Woodward had become a mother, Debbie Eappen is said to have appeared ‘shell-shocked’, responding, “No, I didn’t know that.”
Woodward, from Bridgnorth, Shropshire, has previously said: “I know there are some people waiting for me to have a baby so they can say nasty things.
"It upsets me but that is not going to stop me leading my life. I am innocent.”
Woodward has always maintained her innocence, appearing on BBC programme Panorama to give her side of the story to journalist Martin Bashir following her release.