Applicants are being invited for the illustrious position, once held by Sir Isaac Newton, which will be vacated on October 1, 2009.
But Prof Hawking will continue his work as usual at Cambridge University as Emeritus Lucasian Professor at the university, an honorary title.
A spokeswoman explained it was University policy for professors to "pass the baton" in the year they reach the age of 67.
She said Prof Hawking's diary is already booked up to 2012.
"The post is retiring but Hawking isn't," the spokeswoman said. "Nothing will change. It is merely a formality."
Prof Hawking, 66, will have held the position of Lucasian Professor of Mathematics for 30 years at the time of his retirement.
Isaac Barrow became the first holder of the post in 1664, and notable successors have included Charles Babbage, Sir Joseph Larmor and Sir James Lighthill.
Despite being almost completely paralysed by motor neurone disease, Prof Hawking became one of the world's leading experts on gravity, black holes, and the origins of the universe.
The applied mathematician and theoretical physicist also hit the headlines earlier this year when it was rumoured he could be set to leave Cambridge to join his colleague Prof Neil Turok at the Perimeter Institute in Ontario, Canada.
