Chief executive King and the secretary of state for culture, Olympics, media and sport, appeared at a press conference at Sainsbury's Store Support Centre in Holborn this morning to promote the initiative, which is also sponsored by Adidas.
The 2012 School Games follow on from the long-running Sainsbury's UK School Games which ran from 2006-2011. The four-day event will run in May and takes place in some of the Olympic and Paralympic venues.
Justin King, Sainsbury's chief executive, said: "Our Active Kids programme has been running for over seven years now, we've donated over £100m of equipment to schools."
The initiative aims to give schoolchildren in years three to 13 the chance to experience what it feels like to compete in the Olympic Games.
Hunt said it was important that the government harnessed what was in the commercial interest of brands to get more people playing sport.
He said: "Sainsburys have a very longstanding commitment to getting more young people playing sport and a very longstanding commitment to paralympic sport through the active kids programme and that obviously has public value and public benefit."
Hunt added that with controversy surrounding fat cats and bonusses in big business he welcomed companies "doing the right thing, in this case helping young people into sport".
Asked seperately what he thought of criticism of the involvement of food companies such as McDonald's and Cadbury's with the 2012 Games, Hunt defended the brands.
He said: "I'd say we want to encourage big companies to do the right thing and if there are sporting initiatives that are getting more young people playing sport isn't that a good thing for McDonald's and Cadbury's to be doing? We should be encouraging that and not disparaging it."
Today's announcement was supported by Olympic silver medallist Gail Emms and 2012 Paralympic hopeful Andrew Lapthorne. Young athletes from the City of London Academy in Southwark were also in attendance.
The School Games are run by the Youth Sport Trust and handled by sponsorship agency Fast Track. Fast Track was voted Marketing's Sponsorship Agency of the Year in 2011.
Young entrants will be involved in every aspect of the event with around 2,000 children taking part as competitors, volunteers, officials, reporters and stadium announcers.