Lady Hale said: “We are particularly pleased that you wanted to meet absolutely everybody.
“It is very, very kind of you and everybody appreciates it hugely.”
Charles acknowledged that the pair had caused “a certain amount of disruption” in a speech to all the staff before he left.
He added: “I hope it has given you a slight breather from all of the many cases and all of the difficult publications you have to deal with.”
Lady Hale presented the couple with teddy bears.
“You might possibly know people who might enjoy them,” she said.
Charles told court staff he thought the building, formerly the Middlesex Guildhall, had been converted in a “marvellously sensitive way”.
“I always wondered at the time when this happened how it would turn out,” he added.
Lord Brian Kerr, another Justice, said the visit helped bring the Supreme Court “into public attention”.
He added: “It is very pleasing that they recognised the importance of the work that we do.”
A decade ago the Justices moved out of the House of Lords and across Parliament Square to their new home which had been painstakingly renovated over the previous two years to restore many of its original features.
The establishment of the Supreme Court was a landmark moment in the nation’s constitutional and legal development, separating Parliament from the judiciary at its highest level.
The Justices sat for the first time as a Supreme Court in October 2009 and have gone on to make rulings on the most important and pressing cases.
Lady Hale said Camilla told her she was looking forward to an upcoming trip to Cuba, but was apprehensive about eating the country’s food.
“She said she loved the music and she was interested in the architecture and she did make a remark to say she wasn’t quite so sure about the food,” Lady Hale added.