Mr Biden has a meeting with Mr Putin next week.
"I said I wish we could stay longer, maybe we could hold the cars up a minute, and stuff". I don't think she'd be insulted but she reminded me of my mother. She was very generous.
He said she reminded him of his mother in the "look of her and her generosity".
The queen first met a serving US president, Harry Truman, as Princess Elizabeth in 1951.
Mr Biden accompanied the Officer Commanding the Guard of Honour, Maj James Taylor, and Maj Gen Christopher Ghika to inspect the Honour Guard, before returning to the dais to watch the military march-past.
It generally is frowned upon for anyone to reveal the contents of their private talks with the Queen. The Queen was wearing a Stewart Parvin dress in a floral print jacquard in shades of pink, olive and russet, and she teamed it with a hat by Rachel Trevor-Morgan and the diamond Jardine star brooch. She has welcomed four other USA presidents to Windsor Castle, where she has been isolating during the coronavirus pandemic.
They greeted the Queen on a dais in Windsor's quadrangle before a Guard of Honour gave a royal salute as the U.S. national anthem was played.
He replied: "Yes, we did".
After taking private afternoon tea with the queen on Sunday, Biden is traveling to nearby Brussels for a North Atlantic Treaty Organisation summit, before heading to Switzerland on Wednesday for a meeting with Russian President Vladimir Putin.
The queen had already met the Bidens on their visit to Britain.
The Bidens became the fourth president and first lady the queen has received at Windsor, following the Trumps in 2018, the Obamas in 2016, President George W. Bush and his wife in 2008 and the Reagans in 1982. "We haven't met her yet".
The event comes in the middle of a busy few days for the Queen, who appeared publicly yesterday alongside other senior royals at a reception for leaders as part of the G7 Summit. Some of the soldiers had been involved in the funeral of the Duke of Edinburgh, the queen's husband of 78 years who died just weeks short of his 100th birthday.
Her son Prince Charles and his wife Camilla travelled to the U.S. in 2015 on her behalf and met with Biden when he was Vice President. She has met every serving American president since Dwight Eisenhower - except Lyndon Johnson who did not travel to Britain while in office. It is believed the visit overran by 10 minutes.
Meanwhile, today's carefully-choreographed arrangements to welcome Mr Biden echo the welcome given to Donald Trump three years ago, when the controversial then-US president travelled to Windsor to meet the monarch.
The visit included a Guard of Honour and afternoon tea with the monarch.