The world-renowned physicist, who has motor neurone disease, was described by organizers as "the most famous disabled person anywhere on the planet."
Hawking, who wrote the book "A Brief History of Time", opened the ceremony, which began with a flyover of the stadium by a plane piloted by a war-wounded Afghanistan veteran. Hawking spoke of the quest for understanding the universe.
"Look up at the stars and not down at your feet," Hawking said. "Be curious."
Earlier, the Paralympics torch was accompanied by cheers and prayers as it was carried through London, heading eastward towards the Olympic Stadium. The route included Piccadilly Circus and Westminster Abbey.
Crowds lined streets as the torchbearers carried the flame down Abbey Road, the street made famous by The Beatles.
Some 3,000 performers were recruited for the opening ceremony - the curtain raiser to the highest-profile Paralympic Games in the event's 52-year history.
South Africa's Oscar Pistorius is among the stars set to compete during the 11 days of events. Pistorius made history by becoming the first double amputee to run in the Olympics this month.
The International Paralympic Committee predicts that more than 4 billion people will watch the games on television. With 2.5 million tickets on sale, all events were expected to sell out.
Britain is considered the "spiritual home" of the Paralympics. The first such athletic competition featuring disabled athletes was hosted in the English village of Stoke Mandeville in 1948. The first official Paralympics were held in Rome in 1960.
When the flame was initally lit in the village on Tuesday, London Olympics boss Sebastian Coe paid tribute to Ludwig Guttmann, the German-Jewish neurologist who set up the first wheelchair sports tournament there.
rc/mz, jr (AFP, Reuters)