Welland, a Lancashire-born father-of-four who acted in everything from Kes to Z Cars, won his Academy Award for the screenplay of Chariots of Fire in 1981, famously waving his statue and announcing in his acceptance speech: "The British are coming!"
His family said in a statement that he had suffered from Alzheimer's disease for several years but died peacefully in his sleep.
In a statement released via his literary agent Anthony Jones, his family said: "Colin will be desperately missed by his family and friends.
"Alzheimer's is a cruel illness and there have been difficult times but in the end Colin died peacefully in his sleep.
"We are proud of Colin's many achievements during his life but most of all he will be missed as a loving and generous friend, husband, father and granddad."
Welland, who died last night, is survived by his wife Patricia, four children and six grandchildren.
Chariots of Fire told the story of two athletes in the 1924 Olympics: a devout Scottish Christian who runs for the glory of God, and an English Jew who runs to overcome prejudice.
On winning the award for Best Original Screenplay for the film at the Academy Awards in 1982, Welland warned the American audience: "The British are coming!" - a famous quotation attributed to US revolutionary war hero Paul Revere.
Born Colin Williams in Lancashire, he considered Liverpool his home town.
He studied art in Yorkshire, before attending Goldsmiths college in London, returning to Lancashire to become an art teacher, before his impending marriage motivated him to try his hand at acting.
The British Academy of Film and Television Arts tweeted: "We're deeply saddened to learn that the BAFTA-winning writer and actor Colin Welland has passed away."