Cantwell's first credit came on Stanley Kubrick's 1968 sci-fi movie 2001: A Space Odyssey.
Star Wars creator George Lucas then asked him to design and make prototypes for the Death Star, X-Wing, TIE fighter and Imperial Star Destroyer.
Cantwell's cousin Shannon Eric Denton said he "brought a lot of joy to the world with his art".
Denton added on social media: "And for all of us that knew him he brought a lot of joy being himself."
Cantwell, who also came up with the original design for the Millennium Falcon, was "an incredibly kind human and smart in ways most people dream of", Denton wrote.
Cantwell was born in Colorado in 1932 and gained a degree in animation before going on to study architecture.
During the 1960s space race between the US and Russia, Cantwell worked at the Jet Propulsion Laboratory and Nasa, helping the American public to better understand the flights.
This led to him working alongside TV journalist Walter Cronkite during his historic Moon landing broadcast in 1969, providing a link between him and the astronauts.
Cantwell's interest in both architecture and space saw him prosper in Hollywood, where he worked in special photographic effects for 2001: A Space Odyssey, helping to create the film's dramatic space opening scene.
Star War director Lucas then recruited him, alongside other designers like Ralph McQuarrie, to help create initial models for the original 1977 film.