Kate spoke of her joy during a visit to the Foundling Museum, which is dedicated to the history of the UK's first children's charity and public art gallery the Foundling Hospital, in central London.
Harry and Ms Markle announced on Monday that they are to wed after a 16-month long-distance relationship.
The duchess, who is pregnant with her third child, said: "William and I are absolutely thrilled.
"It's such exciting news.
"It's a really happy time for any couple and we wish them all the best and hope they enjoy this happy moment."
Kate, wearing a navy and white dotted Kate Spade dress and burgundy high heels, met with families and children who use the museum's educational and outreach schemes, and also young care leavers training to run creative workshops.
She spent time talking to youngsters who had made art works, including handmade lanterns and a wishing game, in a joint project with Great Ormond Street Hospital.
She also joined a craft session with toddlers from the Thomas Coram Nursery.
Now known as Coram, the hospital charity was set up in 1739 by Thomas Coram to care for babies who had been abandoned by their parents and between 1741, when the first infants were admitted, and 1954, when the last pupil was placed in foster care, it took in around 25,000 children.
The duchess was shown around the exhibits by Caro Howell, the museum's director, and was told about tokens left by mothers who could not look after their children.
She replied "it's so sad," when told many of the mothers never returned to collect the children or the trinkets.