"I couldn't believe it when I saw who it was. We waved and they waved back," one visitor told The Sun.
"They looked happy and relaxed and waved to everyone on the bus. Charles and the Queen were at Windsor Castle at the same time so they must have met them both.
"It was quite the sight. We knew we might see Charles and the Duchess of Cornwall at the ceremony but never believed we would bump in to Harry and Meghan."
Harry has recently made headlines for suing the UK government for taking away his armed bodyguards.
Prince Harry's suit alleges he "does not feel safe in the UK".
Yesterday's visit has been described as an attempt by the Sussexes at extending the olive branch.
"It is a wonderful opportunity to clear the air and offer an olive branch. After everything that has gone on it must have taken a lot for Harry and Meghan to go to Windsor," Ingrid Seward, editor-in-chief of Majesty Magazine, said about the surprise visit.
"Also Maundy Thursday is a very special day for the Queen as it is about forgiveness. She is not one to hold grudges and I think she would have happily welcomed them with open arms," she added.
It is not known whether Archie, 2, and Lilibet, who the Queen is yet to meet, joined the couple on the trip.