The Australian former Interpol officer has been at the forefront of FIFA's campaign against match-fixing and last month said that 2012 would be a fundamental year in the battle against one of the biggest threats facing the sport.
Eaton will join the Qatar-based International Centre for Sport Security as the organisation's director of sport security in May.
"I am sad to be leaving FIFA, but I am pleased to take with me an experience and knowledge that only FIFA within the current environment can provide," Eaton said in a FIFA statement on Friday.
"I am taking a new challenge that will encompass all sports, many of which could learn from FIFA's approach to combating match fixing."
He has called for greater co-operation from governments and police, saying that match-fixing is the work of organised criminal gangs which football's authorities cannot take on alone.
Under Eaton's blunt leadership, FIFA has offered an amnesty to players who have been involved in match-fixing and come forward with evidence.
"FIFA remains fully committed to the fight against match-fixing, an area where it has undertaken pioneering work," said the FIFA statement.
