Although, joked the 73-year-old physicist, "Unfortunately, Eddie did not inherit my good looks."
Hawking suffers from amyotrophic lateral sclerosis (ALS), a degenerative disease that affects nerve cells in the brain and spinal cord.
He irreversibly lost the ability to speak in 1985 after having a tube inserted into his windpipe during a bout of severe pneumonia and now communicates in instantly recognizable tones using an electronic speech synthesizer.
"Before I lost my voice, it was slurred, so only those close to me could understand [it]. But with the computer voice, I found I could give popular lectures," Hawking said.
"Although it gave me an American accent, I have kept that voice, because it's now my trademark."
Hawking's comments came as he gave a personal guided tour of London's Science Museum
to 24-year-old L.A.-resident Adaeze Uyanwah, who beat more than 10,000 entrants in a competition to be named London's Official Guest of Honor
Redmayne, 32, has been nominated for an Academy Award for best actor for his uncanny transformation into Hawking.
The actor has already picked up an armful of awards for the role, including both the BAFTA and Golden Globe prizes for best actor, and is in the running to take home an Oscar when the winners are announced on February 22.
"The Theory of Everything" follows Hawking from the 1960s during his early days as a bright postgraduate student at Cambridge University to the 1980s when he publishes the seminal "A Brief History of Time," and focuses on his relationship with his first wife Jane and his battle with ALS.
It is based on the memoir "Travelling to Infinity: My Life with Stephen," written by Jane, who is played in the film by Felicity Jones.
Initially, the filmmakers used a voice-box programmed to sound like the one Hawking uses, but after watching an early screening, the physicist was so pleased that he allowed filmmakers to use his voice, according to Newsweek
. "He offered us his voice," Redmayne told Newsweek. "For me, that was the most wonderful thing."
The British actor has confessed to nerves about playing a living legend and told Variety
that he always knew that his toughest critic would be Hawking. But when the lights came up Hawking's nurse wiped a tear way from his face -- and he called the film "broadly true," Variety reported.
During the tour, Hawking said the museum is one of his favorite places and "helped fuel" his fascination with physics.
The physicist showed Uyanwah items from the museum of particular significance to him, including a rare copy of Newton's Principia Mathematica
from 1687 and a reconstruction of a 1953 model of the famous double helix structure of DNA discovered by Francis Crick and James Watson.
"We are now entering a new phase of what might be called self-designed evolution in which we will be able to change and improve our DNA," he told her.
"Now that we have read the book of life, we can start writing in corrections, to make us more intelligent and better natured."
As well as meeting the science legend, VisitLondon.com
's Guest of Honor initiative, part of the "GREAT Britain" campaign
, treated Uyanwah to a private tour of Shakespeare's Globe
theater, a walk down the red carpet at the premiere of "The Second Best Exotic Marigold Hotel" and tea with London Mayor Boris Johnson.
Uyanwah didn't leave her meeting with Hawking -- which she described as something she'll "never forget" -- without taking the opportunity to ask him what he would change about the human race -- and what virtues he would magnify.
"The human failing I would most like to correct is aggression. It may have had [a] survival advantage in cave man days ... but now it threatens to destroy us all. A major nuclear war would be the end of civilization, and maybe the end of the human race.
"The quality I would most like to magnify is empathy. It brings us together in a peaceful loving state."
The eminent thinker finished the tour by telling her that he hoped the objects he'd shown her would remind her to "hold on to that childlike wonder about what makes the universe exist."
"Look up at the stars, and not down at your feet," he said.