LONDON (Reuters) - London 2012 chairman Seb Coe will serve as Prime Minister David Cameron's Olympic legacy ambassador after the Games finish on Sunday, the British government said.

Coe, a former Conservative parliamentarian as well as a double Olympic gold medalist and vice-president of athletics' world governing body, will advise Cameron on how best to secure the long-term benefits of hosting the Games.

Coe will focus particularly on the economic and business benefits.

"Seb Coe has done a brilliant job delivering the best Games ever. Now I want him to help me deliver the best Olympic legacy ever," Cameron said in a statement.

"Legacy has been built into the DNA of London 2012 from the very beginning thanks to Seb. I'm delighted that (IOC president) Jacques Rogge described our legacy plans as a blueprint for future Games hosts.

"I am determined to make the most of the economic opportunities on offer from hosting the Games - making sure that we turn these Games into gold for Britain."

The British government has targeted 13 billion pounds ($20.40 billion) of economic benefit as a result of hosting the Olympics. Britain has enjoyed its best Games medal haul since 1908 and is basking in global appreciation of a successful Olympics.

Coe's role will see him act as a roving global ambassador to help win new trade and investment deals for British businesses as well as advising Cameron on ways to ensure that legacy plans are put into action. ($1 = 0.6373 British pounds)

(Reporting by Alan Baldwin, editing by Mark Meadows)