Kate Middleton is back on royal duty! Credit: AFP PHOTO/POOL/LEON NEAL/Getty Images

Kate Middleton has returned to royal duty for the first time since the announcement of her second pregnancy.

Wearing an Alexander McQueen coat and a Jane Taylor Hat, the pregnant Duchess of Cambridge waved and smiled to well-wishers as she joined her husband Prince William to greet the President of the Republic of Singapore and his wife Mary at London's Royal Garden Hotel on the morning of Tuesday, Oct. 21.

Showing the hint of a small baby bump, the current mom-of-one looked well, despite having suffered from hyperemesis gravidarum, a serious form of morning sickness, for the first three months of her pregnancy.

"I've been looking forward to getting out of the house," the Duchess joked with the Singaporean President, adding, "It's a bit colder than when we last met" (the last time was in Singapore, during their 2012 Asia-Pacific tour).

Yesterday, Kensington Palace confirmed to Us Weekly that the royal couple will welcome their second child in April, 2015. The baby will be a younger brother or sister to their first child, Prince George, 14 months. See the cutest photos of Prince George and his parents.

Middleton's morning sickness had forced her to pull out of a string of royal events in recent weeks, including her scheduled first solo tour to Malta in September, a role Prince William took over as his wife remained resting at home.

But thankfully the Duchess is now on the mend. "The Duchess of Cambridge continues to be affected by Hyperemisis Gravidarum, but her condition is steadily improving," the Palace told Us yesterday.

After greeting their guests this morning, Prince William and Kate then traveled via carriage with the President and Mrs. Tan to Horse Guards Parade, where they received a Ceremonial Welcome from the Queen and the Duke of Edinburgh.

The royals and their guests then continued to Buckingham Palace, taking part in a state carriage procession along the Mall. The Duke and Duchess of Cambridge traveled in the Scottish State Coach, the third in the procession, from Horse Guards to the palace.

Prince William will remain at the palace for lunch, although Kate will not.

Later today, the pregnant royal is due to undertake her second engagement since her pregnancy announcement. This time she will attend the Wildlife Photographer of the Year 2014 Awards Ceremony at the Natural History Museum.