After speaking at the National Mental Health and Policing conference in Oxford yesterday, an audience member congratulated him on the news.
Royals also tend to go for English names that have a royal history and Alice is no different, Queen Victoria's second daughter was called Alice as was Prince Philip's mother (Prince Williams' great-grandmother).
Hyperemesis gravidarum is an unusually severe form of morning sickness that can cause nausea, persistent vomiting, fainting or dizziness that can lead to dehydration - Catherine was was hospitalised when pregnant with Prince George for that reason.
The couple have returned to live in Kensington Palace after an earlier spell in Norfolk, eastern England, enabling them to dedicate more time to their royal duties on behalf of William's grandmother, the queen.
Clarence House, the official account of Prince Charles and Camilla Parker Bowles, retwetted the post as well, adding, "TRH are delighted with the news that the Duke and Duchess of Cambridge are expecting their third child".
On a more serious note, Prince William also made a more direct reference to Kate's current condition.
Harry said he was "very, very happy" for his brother and sister-in-law, telling journalists "it's fantastic". "I haven't seen her for a while but I think I she's okay", he said.
Kate's last public engagement was last Wednesday, on the eve of the 20th anniversary of Princess Diana's death, when she accompanied William and Harry in a tour of a garden at Kensington Palace planted in memory of Diana. "Her Royal Highness will never again do her arranged engagement at the Hornsey Road Children's Center in London today".
No details have been provided as of now regarding when the baby is due.
In London, their residence has been Apartment 1A at Kensington Palace since 2014.
"But she's ecstatic to be expecting baby number three - this is everything she's always wished for".