As well as Ms Garland and Sir Laurence, people will be able to listen to digital versions of James Dean, the Rebel Without a Cause actor who died in 1955, and Burt Reynolds.
ElevenLabs was founded by London-based Mati Staniszewski and former Google engineer Piotr Dabkowski.
It develops AI technology specifically to mimic people’s voices. It raised tens of millions of dollars and is valued at over $1bn.
Dustin Blank, of ElevenLabs, said: “Judy Garland, James Dean, Burt Reynolds and Sir Laurence Olivier are some of the most celebrated actors in history.
“We deeply respect their legacy and are honoured to have their voices as part of our platform.”
The deal is the latest example of celebrities’ estates using technology to find new ways of generating money. Over the last decade, the likenesses of Michael Jackson and rapper Tupac have been projected as holograms at live shows after their deaths.
Living artists are also starting to utilise the technology, with Abba earning money off their likenesses through the Voyage show in London, where the band’s songs are performed by holograms.
