The company runs all of its European markets separately and the win is purely for the company's domestic business.
The pitch, which began in May, also included a review of the company's £5.5 million media planning and buying account.
The media business, which was originally held by Starcom, was moved into Mediaedge:cia two weeks ago.
As well as continuing to create Nintendo's sponsorship idents for programmes such as Channel 4's Modern Toss, Burnett will be briefed to create all of the launch advertising for the forthcoming release of the company's next- generation games console, the Nintendo Wii.
Nintendo is expected to be investing substantially in the console, which is being hailed as the first of its kind. The campaign will include substantial TV advertising as well as poster and print executions.
The WiFi machine is totally wireless and, as well as WiFi internet connection, giving players multiplayer options, has a button-free controller that allows players to feel as if they are really in the game.
For example, in a tennis game, the controller is swung like a tennis racket and the WiFi technology picks up the player's moves.