Announced on 11 December, the "Special Fundamental Prize" was among the second round of physics prizes awarded by the foundation, which was set up earlier this year by Russian billionaire businessman and former physicist, Yuri Milner.
Leading physicists from Cern, the European Organisation for Nuclear Research, were also awarded a $3 million special prize for their role in work that led to the discovery of a Higgs boson-like particle.
These included Imperial College London's Tejinder Virdee and Welsh scientist Lyn Evans, alongside Peter Jenni, Fabiola Gianotti, Michel Della Negra, Guido Tonelli and Joe Incandela.
Prizes from the foundation are now the biggest annual awards in academia, exceeding the 8 million Swedish krona Nobel Prize and ?1.1 million Templeton Prize.
Further awards announced included three $100,000 New Horizons in Physics Prizes for promising young researchers, awarded to Niklas Beisert of ETH Zurich in Switzerland, Davide Gaiotto of the Perimeter Institute in Ontario, Canada, and Zohar Komargodski of Israel's Weizmann Institute of Science.
The foundation also announced winners of the Physics Frontiers Prizes, who will all become nominees for the $3 million 2013 Fundamental Physics Prize, set to be announced at Cern on 20 March.
Laureates Alexander Polyakov and Joseph Polchinski (who received the prize for contributions to quantum field theory and string theory) and Charles Kane, Laurens Molenkamp and Shoucheng Zhang (for work on topological insulators) will receive $300,000 if they fail to win the overall award.
Unlike the Nobel Prize, theories do not have to be verified experimentally to be worthy of the foundation's prizes. Scientists can also win more than once, and there is no limit to how many researchers the cash can be split between.
Professor Hawking, who is director of research at the department of applied mathematics and theoretical physics, was awarded the special prize for his discovery of radiation from black holes and his contributions to quantum physics.
Cern director general Rolf Heuer said the Fundamental Physics Prize underlined the value of fundamental physics to society and that Cern's prize recognised the work of everyone who has contributed to the Large Hadron Collider project over many years.
Earlier this year Mr Milner, who made his billions investing in internet companies such as Facebook, Groupon and Twitter, said he hoped the prize would raise awareness about fundamental physics, which aims to understand the basic laws of nature. The organisation has given away more than $34 million so far.
In a statement Mr Milner said he hoped that the prizes would "bring further recognition to some of the most brilliant minds in the world and the great accomplishments they have produced".