XIX Entertainment existing clients include David Beckham and Andy Murray.
Hamilton had been without a manager since he ended his commercial relationship with his father, Anthony Hamilton, last year.
No financial details of the deal, which is believed to be "ongoing", have been disclosed.
Hamilton agreed the deal with Fuller's company after talking to a number of unnamed agencies.
XIX Entertainment was set up in 2010 after Fuller sold his previous entertainment business, 19 Entertainment, to US company CKX in 2005.
Fuller's clients include Annie Lennox, Jennifer Lopez, Sir Michael Caine and The Spice Girls.
Hamilton drives for Vodafone McLaren Mercedes and will start his fifth season in the sport at the Melbourne Grand Prix on 25 March.
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