They flew in from their home in the US before travelling on to The Hague in the Netherlands for the Invictus Games.
“Being with her, it was great, it was just so nice to see her, she’s on great form," Harry told NBC's Today show.
“She’s always got a great sense of humour with me and I’m just making sure that she’s protected and got the right people around her.
“Both Meghan and I had tea with her, so it was really nice to catch up with her.”
The queen turns 96 on Thursday, just over a year after the funeral of her husband the Duke of Edinburgh.
“Home for me now, for the time being, is in the States and it feels that way," said Harry. “We’ve been welcomed with open arms and have such a great community up in Santa Barbara.”
The couple moved to Montecito, California, after their decision to step down as senior royals in 2020, saying they wanted a new life of personal and financial freedom.
He also returned to the UK to unveil the statue of his late mother Diana, Princess of Wales, on July 1, 2021, with his brother Prince William.
His full interview with NBC is due to air on Wednesday.