The King warmly greeted the American leader in Windsor Castle’s quadrangle shaking hands with Mr Biden as a guard of honour stood nearby.
As the two men shook hands, Mr Biden touched the King’s right arm with his free hand and Charles returned the gesture.
The visit to Windsor was part of a busy day for the president, who is making a layover in London on the way to the Nato summit in Vilnius, Lithuania.
In front of the two men was a Guard of Honour formed of The Prince of Wales’s Company from the Welsh Guards.
The Guardsmen gave a royal salute and the American national anthem was played by the Band of the Welsh Guards when the visiting head of state arrived.
Mr Biden, accompanied by the King, walked onto the grassed area of the quadrangle to inspect the Guardsmen who stood in two rows.