Close family and friends were invited to celebrate the occasion at the Windsor property, where there was face-painting and cake, according to guests.
A spokesman for the couple did not name the family members who attended.
A picture of Lilibet Diana Mountbatten-Windsor, which shows her smiling and dressed in a pale blue frock with a white bow in her hair, was taken by photographer and friend of the couple Misan Harriman, and released by Harry and Meghan on Monday.
The family friend later shared a black and white snap on Twitter of Meghan holding Lilibet alongside the words: “It was such a privilege to celebrate the 1st birthday of Lilibet with my family and hers! Joy and face painting all around.”
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The birthday cake was made by the Sussexes’ wedding baker Claire Ptak, according to a spokesman for the couple.
Harry and Meghan thanked well-wishers, including some who made donations amounting to more than £79,000 in Lilibet’s honour to the World Central Kitchen, a not-for-profit organisation partnered with the couple’s Archewell foundation, the spokesman said.
The organisation has provided support in Uvalde, Texas and Ukraine.
On Friday, the Sussexes made their first public appearance alongside the Windsors since they stepped down as senior royals two years ago, but were absent from many of the Jubilee festivities over the weekend.
The Sussexes were not among those in the royal box at Saturday’s star-studded live concert in front of Buckingham Palace, which was attended by the Prince of Wales, the Duchess of Cornwall, and the Duke and Duchess of Cambridge.
Saturday was Lilibet’s birthday and a spokesperson for the couple had said on the weekend they were spending the day privately.
Lilibet is the Queen’s family nickname, which was first used when Princess Elizabeth was just a toddler and unable to pronounce her own name properly.
One-year-old Lilibet, known as Lili, also has the middle name Diana, which was chosen in memory of her late grandmother Princess Diana, who died in 1997.