In an announcement from Kensington Palace, the royal family is "delighted with the news".
The Duchess experienced hyperemesis gravidarum during her previous pregnancies - an extreme form of morning sickness that can lead to constant vomiting, weight loss, dehydration and depression. Kate, who suffered from the condition with her first two pregnancies as well, is being cared for at Kensington.
Thomas's Battersea will welcome the young prince and his parents on Thursday. Last week the royals toured the garden of their Kensington Palace home to remember the princes' mother and celebrate her contributions to their family and to the monarchy.
An age gap of less than two years between Prince George and Princess Charlotte gave Kate enough time to try for a third before she reached her late 30s, when women's fertility starts to decline more rapidly.
On a royal tour of Poland in July 2017, Kate joked about having a third - after being given a present designed for newborns.
Kate is the eldest of three siblings, and reportedly had a very happy childhood.
Regardless of whether the child is a boy or a girl, the baby will bump Prince Harry down the line of succession to fifth behind Charlotte. "We will just have to have more babies", she said laughing.