The event - titled 'Enlightenment' - will include around 3,000 volunteers, and is billed as a "journey of discovery".
The ceremony is due to begin tonight (August 29) at 8.30pm, but there are fears that the Olympic flame will not arrive in the stadium on time, as it is currently two hours late, reports BBC News.
The 24-hour torch relay began last night in Stoke Mandeville, and there are plans for a possible back-up flame to be lit if it does not arrive on time.
A crowd of around 80,000 people will witness the opener, to be started by The Queen and attended by Prince William and Kate Middleton.
The show will begin with a fly-over by Aerobility, a charity organisation that trains disabled people to be pilots.
Hawking will appear as a guide to Miranda, a character from The Tempest by William Shakespeare throughout the event, while McKellen will play Prospero.
Co-artistic director Jenny Sealey said that viewers will be shown an "exquisite journey of discovery inspired by the wonder of science".
She added: "Both Hawking and McKellen in their narrative talk about what we all need to remember - don't just look down at your feet, look at the stars, be curious."
Fellow artistic director Bradley Hemmings had approached Hawking in late 2011. He said: "We worked very closely with Professor Hawking to develop a series of messages which are very much integrated into the storytelling of the ceremony.
"We have spent time with him in Cambridge and have been so incredibly gratified with him giving his time".
The Opening Ceremony will be broadcast live in the UK on Channel 4 and BBC Radio 5 Live.
Prince Harry has been confirmed to attend a selection of events during the Paralympic Games.