He will play himself as "an intellectual" - complete with "supercharged wheelchair" - called on to give advice to the dysfunctional American family.
According to the cartoon's makers, Bart - slogan, "underachiever and proud of it" - his father Homer and sister Lisa were "overawed" by the author of A Brief History of Time.
Prof Hawking flew to Hollywood last week to film the episode, which is set to be broadcast in the spring. An animated figure of the black holes expert is now being drawn - in the series' trademark yellow - but the script was programmed into the physicist's computer and will be spoken with his distinctive electronic voice.
The plot line revolves around Mensa, the society for high IQs. A group is set up in the Simpsons' home town of Springfield but goes off the rails, giving a bad name to clever people, and the professor is called in to save the day.
"He comes in to make a commentary on the universe as a whole and intellectuals," explained Bonnie Patila, the producer of the show. "He plays himself - it's a show that has to do with intellectuals and we don't know anyone more intellectual than him."
Although the initial hour-long filming session was a one-off, the producers are now considering giving Prof Hawking regular appearances.
Friends say the maths genius "greatly enjoyed" his Hollywood experience and would like to get more acting parts. While on the Simpsons set, he met the actors who play the characters and Matt Groening, creator of the series.
Prof Hawking joins an illustrious list of celebrities who have appeared in the long running series - from Kim Basinger, James Woods, U2 and half the Beatles to former president Bush. But he provoked more interest than any of them.
"Everyone wanted to meet him," Ms Patila said. "We are all huge fans - he was great fun."Reuse content