Wearing a white Givenchy dress and black and white Philip Treacy hat, the new Duchess of Sussex and her husband were accompanied in the carriage by Harry's uncle Edward, the Earl of Wessex, and his wife Sophie.
Thousands of racegoers cheered the newly-weds, who married a month ago in a glittering ceremony at the nearby Windsor castle.
They later presented a trophy to jockey Frankie Dettori who won the St James's Palace Stakes on Without Parole.
The royal carriage procession was led by the Queen, 92, wearing a bright yellow coat and hat.
Earlier on Tuesday, Buckingham Palace announced that Elizabeth's granddaughter Zara Tindall had given birth to her second daughter, the monarch's seventh great-grandchild.
(Reporting by Anu Shukla; editing by Stephen Addison)
