Hawking, diagnosed with motor neurone disease at the age of 21 and told in 1963 he had two years to live, began the ceremony by reading from the stage.
"Look up at the stars and not down at your feet. Be curious," Hawking said from his wheelchair, speaking through his famous computerised voice system for communication.
The London Paralympics will host the biggest number of athletes since their official birth in 1960 at the Rome Games, with 4,280 competitors representing 164 nations compared to 400 participants from 23 countries in the Italian capital.
In scenes like those which gripped the world during the July 27 opening extravaganza at the Olympic Stadium in east London, a similarly inspiring and breathtaking show left the 80,000 fans and millions of TV viewers open-mouthed from the start.
Queen Elizabeth declared the Games open following the mammoth procession of athletes into the Olympic Stadium and Inter-national Paralympic Committee president Philip Craven's speech.