The BBC confirmed his death Monday, but did not report the cause of it.
The son of "My Fair Lady" actor Rex Harrison was best known for his 1968 Oscar-winning hit song "The Windmills of Your Mind" from "The Thomas Crown Affair" film soundtrack.
Harrison lived most of his life in the United States where he starred in the TV series "The Girl from U.N.C.L.E." and recorded hit songs like "A Young Girl" and "Suzanne."
"I was part of the 'British Invasion' spearheaded by The Beatles. I bought a nice house in Los Angeles," he wrote on his website. "There was another U.S. charts record and four years of endless TV appearances, theater tours and star-studded social occasions."
However, he went on to say he "didn't like being a celebrity" and spent his later years working in construction before moving back to the United Kingdom about a year ago, the BBC said.