The 36-year-old actress accompanied the 33-year-old royal in Nottingham on Friday where they made their first joint appearance as an engaged couple. "The Queen has always put duty first and Prince Charles and Prince William have learnt from her".
The city was overrun with crowds of people, members of the press and photographers ahead of the couple's visit.
Asked what she thought of the engagement, she added: "We really wish them all the very best - they're a lovely couple".
When the fan replied, "Unbelievable", Harry laughed and repeated, "Unbelievable!"
The couple, who will be married at St George's Chapel, Windsor Castle, next May, are planning to tour the United Kingdom in the six months leading up to their wedding so the former actress can get to know her new home.
Mary Cooper, 60, who had been waiting to see the prince and his bride-to-be since before 9am, said: "I think it's absolutely wonderful that both he and his brother have found happiness".
"This is good. I'm excited to have some Americans in the royal family", US student Mark Arnold, who is now studying at Nottingham University, told Reuters.
In the central English city of Nottingham, Harry and Markle, both wearing long navy overcoats, greeted hundreds of smiling well-wishers waving British and US flags, chatting and shaking hands with onlookers who braved freezing weather to welcome them. They will then take in other engagements in the city.
At their first sit-down interview after they announced their engagement, the difference between them and Will and Kate during their first post-engagement interview was even more striking.
She said: "It paid off - I knew they'd be in London, doing something, and it's been about a year since they started properly dating".