Sir Alan was known for a string of hit films in the 70s and 80s, including Bugsy Malone, Fame, Midnight Express and Mississippi Burning.
He also made the 1996 musical drama Evita, which starred Madonna.
Following the news Sir Alan had died on Friday morning following a lengthy illness, the singer posted an emotional message, thanking him for “pushing her to her limits”.
Sharing a photo of them together on set, Madonna wrote on Instagram: “I was so sad to hear about the passing of Alan Parker.
“One of the greatest directors iI’ve ever worked with—on the film Evita. He taught me so much, believed in me, pushed me to my limits and made an incredible film! Thank you!”
Antonio Banderas starred in Evita alongside Madonna and described Sir Alan as a “great director”.
Lord Andrew Lloyd Webber also worked with Sir Alan on Evita and said he was “one of the few directors to truly understand musicals on screen”.
Singer Peter Gabriel worked with Sir Alan on 1984 drama Birdy, creating the film’s score. The former Genesis singer said the late director had a “serious impact” on his life.
He said: “He was so encouraging, passionate and dedicated to saying something real with his films, and all delivered with his gentle and timely sense of humour. I only ever heard great things from all those he worked with.”
Many other famous names also shared tributes online...
During a career notable for the variety as well as the quality of his work, Sir Alan won 19 Baftas, 10 Golden Globes and 10 Oscars.
Sir Alan wrote and directed his first feature film, Bugsy Malone, in 1975 – a musical pastiche of Hollywood gangster films of the 1930s with a cast of children.
Sir Alan’s second film, 1977’s Midnight Express, won two Oscars, six Golden Globes and four Baftas.
In 1981, he directed Pink Floyd – The Wall, the feature film adaptation of the band’s successful rock album, which became a cult classic among music fans.
In November 1995, he was made a CBE for services to the British film industry and he received his knighthood in 2002.
Sir Alan received the Bafta Academy Fellowship Award, the body’s highest honour, in 2013.
Sir Alan was born in Islington, London, on February 14, 1944, and began his career in advertising as a copywriter.
He graduated to writing and directing commercials, and in 1974 moved into long form drama when he directed the BBC film, The Evacuees, written by Jack Rosenthal.
He is survived by his wife Lisa Moran-Parker, his children Lucy, Alexander, Jake, Nathan and Henry, and seven grandchildren.