A statement from Buckingham Palace said, "Her Majesty remembers with great warmth her meetings with Mr Mandela.
"He worked tirelessly for the good of his country, and his legacy is the peaceful South Africa we see today."
CLICK ON PHOTOS FOR FULL GALLERY
Prince Charles also paid tribute to the iconic former leader, describing his as the "embodiment of courage and reconciliation".
"He was also a man of great humour and had a real zest for life," the Prince added.
"With his passing, there will be an immense void, not only in his family's life, but also in those of all South Africans and the many others whose lives have been changed through his fight for peace, justice and freedom.
"The world has lost an inspired leader and a great man. My family and I are profoundly saddened and our thoughts and prayers are with his family."
Prince William and Kate Middleton were informed of Mr Mandela's passing while they were attending the premiere of Mandela: Long Walk To Freedom.
Speaking after the film, the Duke of Cambridge said, "We were just reminded of what an extraordinary and inspiring man Nelson Mandela was, and my thoughts and prayers are with him and his family right now."
The death of the iconic statesman was announced on South African national TV by the country's president Jacob Zuma.
"Our nation has lost its greatest son," he said. "Although we knew this day would come, nothing can diminish our sense of a profound and enduring loss."
He said that Mr Mandela — known affectionately by his clan name Madiba — wonld receive a full state funeral, and that flags would be flown as half-mast.