Clarke, who moved to Scotland in 1947 to teach at the Edinburgh College of Art, was awarded an MBE in the New Years Honours list. He was also recently honoured by the RSA with a show celebrating his 100 years.
A spokesman for the Academy said the artist passed away on Monday. He added: "Derek Clarke held a special place at the Academy, having taught generations of fellow Academicians during his hugely active career at Edinburgh College of Art, including Elizabeth Blackadder and John Bellany.
"The RSA were delighted to have held a highly acclaimed and successful exhibition of his works in January last year.
"The exhibition was greeted with great enthusiasm by lovers of painting from all over the world."
He added: "He was delighted to have received the MBE earlier this year, an honour that recognised his long and dedicated service to visual arts in Scotland and further afield."
Born in Longthorpe near Peterborough on the last day of 1912, Mr Clarke was educated at Ampleforth College and attended Slade School of Art in London from 1931 to 1935.
In the Second World War he fought in the Durham Light Infantry and served in Tunisia.
In 1947, he was invited by Robert Lyon, Principal of Edinburgh College of Art at the time, to join the staff of its Drawing and Painting School.
His exhibition at the RSA in early 2013 displayed his portraiture, paintings of family groups, landscapes, including the rock scenery of the north west Highlands of Scotland, animals and religious themes.