Some 3,000 volunteers took part in the show, which organisers have entitled Enlightenment
The Queen has declared the London 2012 Paralympics officially open, during a spectacular opening ceremony watched by some 80,000 spectators.
Britain's first Paralympic Games gold medallist, Margaret Maughan, 84, had the honour of lighting the cauldron.
Paralympics chief Lord Coe told the crowd: "Prepare to be inspired, prepare to be dazzled, prepare to be moved."
Earlier, athletes paraded around the Olympic Stadium, with ParalympicsGB entering last to huge cheers.
'Games to remember'
The opening ceremony signalled the start of 11 days of competition by 4,200 athletes from 164 countries, including more than 300 athletes from the home nation.
Wheelchair basketball, shooting, swimming and track cycling are among the events set to feature on the opening day.
Continue reading the main story
Analysis
Michael HirstBBC 2012
From Stephen Hawking, the Hadron Collider and the Big Bang, to the biggest apple bite, this was a very different opening to that of the Olympics.
It may not have cost as much to put on, but it was just as ambitious.
There were echoes of the Olympics with roles for Shakespeare's Tempest and Tom Heatherwick's cauldron, as well as royals, flags and a parade of elite athletes.
But though the light panels in the crowd created the same spectacular effect as in the Olympic opener, they have now become known as Paralympixels.
At the Olympics opener, the key excerpt from The Tempest was Caliban's tribute to the "Isles of Wonder".
Tonight, it was Miranda's marvelling at "how beauteous mankind is" in her brave new world speech.
This was a ceremony that was more nuanced in its celebration of elite sport. A celebration of diversity. But no less of a celebration for that.
Lord Coe told the crowd at the east London stadium: "It is my great honour to say welcome home to the Paralympic Games."
He said Britain "was ready" and the crowds in attendance would be "unprecedented", adding: "These will be a Games to remember."
Eight members of the British under-22 wheelchair basketball team were given the honour of carrying the Paralympic flag into the stadium. It was raised by members of the armed forces, before the Queen declared the Games open.
British swimmer Liz Johnson, a medallist from Beijing 2008, wheelchair rugby judge Richard Allcroft and David Hunter, who is coaching the ParalympicsGB equestrian team, each stepped forward to take the official oaths on behalf of competitors and officials.
At the close of the ceremony, 24-year-old Royal Marine Commando Joe Townsend - an aspiring Olympic triathlete, who lost both legs while serving in Afghanistan - descended on a zip wire into the stadium from the top of the nearby Orbit tower.
He handed the flame to David Clarke, a member of the ParlympicsGB five-a-side football team, who passed the torch to Ms Maughan, who won gold in archery at the 1960 Rome Paralympics.
She lit a tiny flame on the ground, igniting more than 200 copper petals. Long stems then rose towards each other to form a cauldron, signifying unity.
'Big bang'
The ParalympicsGB athletes earlier entered the stadium to David Bowie's Heroes, led by Peter Norfolk, the two-time Paralympic wheelchair tennis champion, who carried the union jack. He later described it as a "wow moment".
Continue reading the main story
Paralympics in numbers
- 4,280 athletes from 166 countries are to compete throughout the 11 days of sport
- Almost 300 athletes will represent ParalympicsGB
- Over 2.4 million tickets have been sold so far - including half a million to visitors from abroad
- There are 503 gold medals to be won in 21 sports
In one heart-stopping moment during the show, six Paralympians and former competitors - including Baroness Tanni Grey-Thompson - were flown into the stadium in gold wheelchairs.
Disabled ex-serviceman David Rawlins flew a twin-engined Tecnam P2006 light aircraft over the stadium to kick off the proceedings.
A sphere ignited the "big bang" - something which Prof Hawking, a world-renowned physicist who has motor neurone disease, has written about extensively - to start the show and fireworks lit up the stadium.
Professor Hawking and actor Sir Ian McKellen played prominent roles in the ceremony, which also featured a host of deaf and disabled artists, local children and performers newly-trained in circus skills.
Some 3,000 volunteers took part in the event, which organisers entitled Enlightenment and said was "profoundly about science and humanity".
Throughout the ceremony, Prof Hawking acted as a guide to Miranda - a character from William Shakespeare's play The Tempest, who was central to the show - while actor Sir Ian played Prospero, another character from the play.
Inspired by uncertain British weather, umbrellas were also a big theme in the ceremony, which was described as "both spectacular and deeply human" by organisers.
The Queen was welcomed by Sir Philip Craven, President of the International Paralympic Committee, before the union jack was carried in by representatives of the armed forces.
It is the first time the monarch has officiated at the openings of both the Olympic and Paralympic Games.
Teams from all 164 countries paraded into the stadium to music mixed and played by three London-based DJs.
The Paralympic torch began its journey in Stoke Mandeville, Buckinghamshire, the spiritual home of the Paralympic Games, on Tuesday night.
The torch had earlier been delayed but Games organisers Locog confirmed the flame arrived at the stadium in time to light the cauldron.
UK Sport and the British Paralympic Association have set a minimum target of 103 medals this time from at least 12 sports, including swimming, athletics and rowing and hopes are high that ParalympicsGB will emulate the success of Team GB.
Prime Minister David Cameron says the Paralympics will "inspire a lot of people and change people's views on disability"
Britain finished second in the medals table at the 2008 Games in Beijing, winning 42 golds, 29 silvers and 31 bronzes. China were top with 211 medals, of which 89 were gold.
More than 2.4 million tickets for events have already been sold, including half a million to overseas visitors.
In a statement released before she opened the Games, the Queen said: "It is with tremendous pride that the people of London and the United Kingdom welcome the world to the London 2012 Paralympic Games.
"The Games are returning to the country where they first began, more than 60 years ago.
"We look forward to celebrating the uplifting spirit which distinguishes the Paralympic Games from other events, drawing on Britain's unique sporting heritage."
