Charles and the Duchess of Cornwall welcomed Mr Trump and First Lady Melania in the garden for tea at their official residence at 4pm on Monday.
The two couples posed for a picture in the morning room before moving to private quarters for tea.
Mr Trump and Charles appeared at ease with one another as they stood in front of a mantelpiece to have their picture taken with their wives.
As the couples made their way into the room, a photographer in the small group of media dropped her flash diffuser.
Charles laughed as he picked it up, remarking: “It looks like an ice cream.”
The photographer, who was from the US press pool, replied: “Sorry sir, my apologies.”
The two men entered the room first and the president stopped and smiled at the waiting press.
Mr and Mrs Trump shook hands with officials, including the Queen’s equerry and Michael Vernon, controller at the Lord Chamberlain’s office.
The couple were then directed to stand in front of the mantelpiece for a photograph.
Mr Trump held out his left arm, indicating to Charles to stand on his left.
Charles and the president appeared to share a couple of jokes with one another as they could be seen smiling broadly, and at one point Charles laughed.
Mr Trump adjusted his suit jacket and tie as he stood in place for the photo.
At the end the president said: “Thank you very much everyone.”