Concerns over safety and the threat of protests or an attack had dogged the organisers of the 2012 festival of sport in the run up to the Games, especially after it emerged not enough security staff had been recruited, forcing the army to step in.
It was the biggest peacetime security operation Britain has implemented.
"The passion and professionalism of the volunteers has been matched by the fantastic work of the armed forces and the police, who have worked tirelessly to deliver a safe and secure Games," Cameron said in remarks supplied by Downing Street before delivery.
Cameron, whose government faced domestic criticism about the preparations and costs for the sports bonanza, said the Games had helped to show the very best of Britain to the rest of the world.
Trailing only the United States and China, Britain won 29 gold medals in the Games, its best result in 104 years, helping to divert some attention from the worst economic crisis since the Great Depression and the unpopularity of Cameron's government.
Cameron has seen his popularity ratings slump in recent months. An August poll showed 59 percent of voters disapprove of the government's record while just 25 percent approved.
The poll, carried out by YouGov, showed 44 percent of people would vote for the main opposition Labour Party, while 34 percent would vote Conservative and 10 percent Liberal Democrat.
But Britain's medal haul and popular enthusiasm by a broadly successful Olympic Games have eased - at least for a few weeks - broader domestic concerns over Britain's long-term decline.