Hamilton's move from McLaren to Mercedes came amid suggestions that the Brackley-based outfit was offering him a higher retainer than his current team - as well as greater commercial freedom to find personal sponsors.
However, Brawn says that Hamilton's motivation to move teams had nothing to do with money – and was instead about finding a new challenge in his career.
"There is a competitive market for drivers and Lewis is as competitive as anyone else in that respect. But Lewis didn't come here because we offered more money - because we didn't," Brawn told Sky.
"I think, first and foremost, Lewis is a racing driver. That has to be the key to everything. If he's not successful as a racing driver, none of the other stuff can happen.
"Everybody involved here and involved with Lewis recognised that, first of all, he has to be a successful racing driver. Because if he's not a successful racing driver, nothing else can happen. That's the key thing."