Johnson's most famous compositions include themes from The Avengers, Animal Magic, The Professionals, and This is Your Life. He also worked on the 1960’s political satire film, Dr Strangelove.
His family said in statement that the musician died “peacefully in his sleep” on Tuesday 16th January, "leaving behind a legacy that will forever resonate in our hearts."
"Laurie's music touched the lives of millions around the world. Throughout his illustrious career, he composed numerous iconic scores, themes and soundtracks that graced our lives across film, TV, theatre and radio," they said.
"We remember Laurie as an extraordinary individual who embraced life with passion and brought joy to so many.
“His kindness, compassion and infectious sense of fun and laughter will be profoundly missed by all that knew him."
His family added that he was "dearly loved by many" and is "sorely missed" by his wife Dot, daughter Sarah, son-in-law Richard and grandson Lawrence.