Markle, who became Duchess of Sussex after the Royal wedding, joined the new Duke to travel from Windsor Castle to nearby Frogmore House.
The Royal bride chose a "striking" white halter neck designed by British designer Stella McCartney as her second dress of the day.
It was described as a bespoke lily white high neck gown made of silk crepe.
The newlyweds were on their way to an "intimate" evening reception hosted by the Duke's father, Prince Charles.
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Harry drove Meghan through the Windsor Great Park in a open-top, silver blue Jaguar E-type from the 1960s that has been converted to run on electric power. He was dressed in formal black tie.
The car's number plate bore the date of the wedding – E190518.
Photographs taken as they departed the castle show the Duchess wearing a large emerauld ring, similar in style to one owned by the late Princess of Wales, Diana.
Meghan wore shoes from Aquazurra made in silky satin, with nude mesh, with soles painted in baby blue.
Her hair, styled for the reception by George Northwood, was in a relaxed up do, and she tucked loose strands behind her ears amid the breeze as they drove through Windsor's estate.
Phillipa Lepley, a couture wedding dress designer, said: "Meghan's second dress is another clean, perfectly balanced but more sexy, halter neck fluid dress.
"It is an extremely striking frock which lets her shine beautifully, and once again it is not wearing her.
"It highlights her stunning face and gorgeous complexion, in brilliant white. The strong bare shoulders are perfectly counterbalanced by the high neck.
"The train is elegant and adds a classic, timeless feel and keeps her as 'the bride'. Meghan looks in control of her destiny and knows her style."
As a designer, McCartney is known for clean lines, sharp tailoring and understated styles. She was awarded an OBE by the Queen in 2013.
Her father Sir Paul McCartney was also knighted in 2004 and was named a Companion of Honour by the Queen for his services to music.
In McCartney, Markle has chosen a designer who is committed to sustainability and is an advocate for animal rights, and who uses vegetarian alternative materials in many of her designs.
The Duchess's evening appearance followed the earlier reveal of her wedding dress, a bateau-necked pure white gown with long bridal train, designed by French fashion house Givency.