Prof Hawking, who has motor neurone disease (MND), has previously been regarded as being less supportive of the right to die, saying it was a mistake as "there is always hope".
In an interview that will reignite the heated debate surrounding euthanasia, the 71-year-old theoretical physicist and cosmologist told the BBC: "We don't let animals suffer, so why humans?"
He said: "I think those who have a terminal illness and are in great pain should have the right to choose to end their lives and those who help them should be free from prosecution.
"But there must be safeguards that the person concerned genuinely wants to end their life and they are not being pressurised into it or have it done without their knowledge or consent, as would have been the case with me."
Prof Hawking was diagnosed with his disabling and incurable condition at the age of 21, when he was told that he had just two or three years to live.
Following a bout of pneumonia in 1985, he was placed on a life support machine which his first wife, Jane Hawking, had the option to switch off.
Recovering from the infection, Prof Hawking went on to complete his popular science best-selling book, A Brief History of Time, which has sold more than 10 million copies worldwide.
Only 5% of people with the kind of MND he has - called amyotrophic lateral sclerosis (ALS) or Lou Gehrig's disease - survive for more than a decade after diagnosis.
Referring to euthanasia in 2006, he said: "The victim should have the right to end his life, if he wants.
"But I think it would be a great mistake.
"However bad life may seem, there is always something you can do, and succeed at.
"While there's life, there is hope."