Bafta said it was "saddened" to hear of Stamp's death and highlighted his two Bafta nominations in 1963 and 1995.
His Superman co-star Sarah Douglas described him as "beyond gorgeous and talented".
"So saddened to learn that Terence has left us," she wrote on Instagram.
"I learnt so very much from him. What a start to my career to have spent so many months in his company.
"My love and heartfelt condolences to all who cared for him. What a loss."
Born in Stepney, east London, to working-class parents on 22 July 1938, Stamp attended grammar school before pursuing a career in advertising.
After securing a scholarship for drama school, he shot to fame in the 1960s, making his debut playing the titular role in Billy Budd, a 1962 film about a naive young seaman in the 18th century.
His performance earnt him an Oscar nomination for best supporting actor and a Golden Globe for best newcomer.
He went on to make a name for himself as a villain, with stand-out performances in Superman and Superman II as General Zod, kidnapper Freddie Clegg in The Collector, and Sergeant Troy in Far From the Madding Crowd.
During his heyday in the 1960s, Stamp was known for his good looks, fashion sense and high-profile girlfriends, including actress Julie Christie - who he later starred alongside in Far From the Madding Crowd - and supermodel Jean Shrimpton.
His relationship with Christie only lasted a year but was immortalised by the Kinks in the song Waterloo Sunset with the line "Terry meets Julie", believed to reference the pair.