It comes after the monarch, 95, marked her birthday at the annual Trooping the Colour ceremony on Saturday and attended events at the G7 Summit with the Prince of Wales, the Duchess of Cornwall, and the Duke and Duchess of Cambridge.
The Bidens were welcomed by a Guard of Honour in the Quadrangle of Windsor Castle as they arrived, where the Queen’s Company First Battalion Grenadier Guards gave a royal salute, and the US National Anthem was played.
The Bidens walked into the castle with the monarch via the Sovereign’s Entrance.
The presidential jet Air Force One took the Bidens to Heathrow from Cornwall before they were flown by helicopter to Windsor.
WATCH: The Queen taps her feet during Trooping the Colour
The President and First Lady arrived at Windsor Castle on their helicopter, Marine One.
The couple landed just before 5PM, a few minutes ahead of schedule.
KEEP CLICKING FOR MORE PICTURES...
The Queen wore a beautiful pink Stewart Parvin floral print dress for the special occasion and appeared in good spirits. She accessorised with a hat by Rachel Trevor-Morgan and the diamond Jardine star brooch.
The Queen greeted the couple in the castle quadrangle shortly after they arrived in Windsor on Sunday.
They first met on Friday when the Queen attended a reception for G7 leaders at the Eden Project.
Asked by the press what they spoke about during his Windsor visit, President Biden replied: "She said, 'What’s it like in the White House?' I said, 'Well it’s magnificent but it’s a lot of people'."
He also said that he had invited the Queen to the White House.
Bright sunshine greeted the Bidens as the arrived in Berkshire, and the President accessorised his smart suit with sunglasses as a result.
The military put on a spectacular display in honour of the historic meeting.
The Queen and the First Lady enjoyed a conversation during their first official meeting.
Dr Biden looked stunning in a powder blue dress and matching blazer which she wore with a pair of delicate pointed-toe heels and a dazzling silver brooch.
The Guard of Honour gave a royal salute before playing the American national anthem.
In recent years, the monarch has welcomed a number of US Presidents and their wives to Windsor Castle, including Donald and Melania Trump in 2018, Barack and Michelle Obama in 2016, George and Laura Bush in 2008, and Ronald and Nancy Reagan in 1982.
The President inspected the Guard of Honour, accompanied by the Officer Commanding Guard of Honour, Major James Taylor and Major General Christopher Ghika.
The Queen, President Biden and First Lady Dr Jill Biden viewed the military 'march past' from the dais.
The President and Dr Biden put their hands over their hearts as the U.S National Anthem was played.
The Queen and the Bidens appeared to get on well during their first joint official engagement.
President Biden later told the press that they had enjoyed a good conversation.
He said: "We had a long talk. She was very generous. I don’t think she’d be insulted but she reminded me of my mother. In terms of the look of her and just the generosity."
He added: "She was very gracious."
After their official greeting, the couple then joined the Queen for tea in the Oak Room at her Berkshire residence.
Mr Biden walked alongside the Queen who said to the President: "You completed your talks."
He replied: "Yes we did."
Before going inside, the Queen introduced the Bidens to her lady-in-waiting Dame Annabel Whitehead.
Make sure you never miss a ROYAL story! Sign up to our newsletter to get all of our celebrity, royal and lifestyle news delivered directly to your inbox.