Excited crowds cheered as the couple greeted well-wishers ahead of a visit to a World Aids Day charity fair hosted by the Terrence Higgins Trust.
They split up to talk to people lining both sides of their route and were given cards, flowers and chocolate.
After the charity fair, they met head teachers at a nearby school.
Well-wishers gathered in the city ahead of the visit to catch a glimpse of the couple, including Helena Bottomley, Zoe Scott and Carole Bingham, from East and West Bridgford.
Ms Scott said: "We love the royals. We are genuinely happy for Harry."
"We all had our children at the same time as Diana [Princess of Wales] so we feel a real allegiance. She would be so thrilled," said Ms Bottomley.
The couple announced their engagement on Monday and are due to marry at Windsor Castle in May.
One of the people Prince Harry stopped to speak to was Julie Ball, 51, of Netherfield, who said the prince had commented on her Santa gloves.
"He said 'great gloves' and pulled one down over my fingers," she said. "I said they're from Primark for £3.
"When Meghan walked past she said the same thing. She said, 'We have the same taste.'"
Another member of the public shouted to Prince Harry: "How does it feel being a ginger with Meghan?"
"It's great isn't it?" The prince replied.
Dickie Arbiter, former royal spokesman, told the BBC the couple took their time to talk to as many people as possible on their 30-minute walkabout.
University of Nottingham students Raushana Nurzhubalina, from Kazakhstan, and Jenn Galandy, from Canada, set their alarms for 06:00 GMT to get a prime spot to try to see Prince Harry and Meghan Markle.
"It is such an honour to see the royals," Ms Nurzhubalina said.
"I'm also a fan of Suits, so it is a chance to see a star of that too."
Royal fan Irene Hardman had a goody bag ready to hand over to the couple, including copies of the local paper and two fridge magnets "so they don't fight over it".
Speaking afterwards, the 81-year-old said: "I cried - she's wonderful, and it's fantastic. They're so genuine."