The couple will present the winning trophy for the 4.20pm race, the St James' Palace Stakes, said the official Royal Ascot programme.
Harry and Meghan were next, with the Earl and Countess of Wessex, and waved as they travelled past the packed stands on their way to the royal box.
Meghan Markle arrived wearing a cream coat, with a cream and black hat, while the Queen wore yellow.
Prince Harry playfully called out jockey Frankie Dettori after he planted a kiss on Meghan Markle's hand at Royal Ascot on the first of the five-day event which was attended by the royal family. "The Duchess of Sussex's latest outfit splits opinion".
The dad-of-two, who watched the American actress tie the knot with her Prince on TV at his home in Birmingham, West Midlands, said: 'Meghan looked fantastic.
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Clare is the first female Artistic Director at the historic French fashion house Givenchy and was chosen to design the dress for the wedding of the year after meeting Meghan earlier this year.
She went for a monochrome look, with black shoes, belt and bag, and black trim on her Treacy hat.
In fairness, the inside story did describe the dress as "pitch perfect" for the occasion, suggesting women will take inspiration from the look for the upcoming season at Ascot, the English equivalent of the spring racing carnival (with larger hats).
For the third time since joining the British royal family just weeks ago, Meghan chose to wear a Givenchy design.
They've only been married a few weeks but Prince Harry, 33, is already having to warn men away from his stunning wife, Meghan Markle.
Prince Harry and Meghan Markle joined the Queen for the first day of the Royal Ascot 2018 on Tuesday.
It will be their first royal engagement overseas.