The British actor shot to stardom in 1988 as Bruce Willis’s adversary Hans Gruber in Die Hard, and went on to gain a new generation of fans as Professor Severus Snape in the Harry Potter series of films.
A family statement said: “The actor and director Alan Rickman has died from cancer at the age of 69. He was surrounded by family and friends.”
His death comes just days after rock star David Bowie also died from cancer at the same age.
Thompson said her tribute was “hard to write because I have just kissed him goodbye”.
In 2003’s Love Actually they played married couple Harry and Karen.
“What I remember most in this moment of painful leave-taking is his humour, intelligence, wisdom and kindness. His capacity to fell you with a look or lift you with a word,” she wrote.
She called him “the ultimate ally” in life, politics and art, saying she trusted him absolutely.
• OBITUARY: Alan Rickman, actor
“He was, above all things, a rare and unique human being and we shall not see his like again,” she wrote.
Potter author JK Rowling tweeted condolences to his wife Rima, writing: “My thoughts are with Rima and the rest of Alan’s family. We have all lost a great talent. They have lost part of their hearts.”
Potter cast members Daniel Radcliffe and Emma Watson also both paid respects.
Radcliffe called him “undoubtedly one of the greatest actors I will ever work with”, while Watson posted on Facebook: “I’ll really miss our conversations. RIP Alan. We love you.”
Rickman was a popular star of stage and screen, and worked both behind and in front of the camera, with some of his work still to be released.
His new film – Eye In The Sky – in which he stars with Dame Helen Mirren and Aaron Paul is set to open in UK cinemas on 8 April, according to IMDb. The star had also completed another film set for release later this year called Alice Through The Looking Glass.
His career began on the stage after he graduated from Rada, and he frequently returned to the theatre throughout his career.
Hailing from a working-class London family, he supported himself as a dresser before finding work with the Royal Shakespeare Company.
His CV showcases a glittering career spanning almost four decades and featuring a list of hit films from Truly Madly Deeply (1990) to theatre credits including Private Lives and Antony And Cleopatra.