The agency won the business after a five-month pitch process that also involved Carat, Starcom Motive and ZenithOptimedia.
Initiative triumphed after a final stage shoot-out against Starcom MediaVest Group.
The agency currently handles Vauxhall and Daewoo but the £22 million Saab account will move from Universal McCann. Vauxhall spends £69 million in the UK and Daewoo £7 million.
General Motors called the pitch as part of a review of its European media needs on a market-by-market basis.
Initiative's pitch team was led by the managing director, Gary Birtles, who has run the Vauxhall account for nine years. Patrick Dunster, the marketing communications manager at Vauxhall Motors, said: "We've been through an intense pitch process and Initiative proved to be the best."
Jerry Hill, Initiative's chief executive, added: "The process has rigorously tested all aspects of the communication planning and buying output of the agencies involved, and we are thrilled to have been appointed to work across all of General Motors' UK business at a time when the client is going through such a dynamic period."
Initative has also won the £5 million ICI media planning and buying account.
The £3 million Dulux business was previously with PHD and the Polycell and Cuprinol accounts were held by Carat. Naked Communications will work on the communications strategy for Dulux.