He won an Oscar for the stirring score to 1981's Chariots of Fire.
Paying tribute, Lord Puttnam, who produced the film, told the BBC Vangelis had created "a new musical landscape".
US composer Austin Wintory wrote on Twitter that Vangelis "changed an entire era of music".
Oscar-nominated British musician Daniel Pemberton said it was hard to underestimate the colossal impact of Vangelis on modern film music.
"It is also hard to understand how groundbreaking Chariots of Fire was. A period British film with a phenomenal synth score," he added.
