The senior investment analyst had been suspended earlier this year as Gartmore examined the way commissions had been allocated to brokers.
While he has since returned to the firm, the FSA has decided to conduct its own investigation into the matter.
Mr Rambourg said his decision to quit to cooperate with the probe had been a "very difficult and personal" one.
"I have been faced with a challenging set of circumstances which has resulted in me not being able to optimally fulfill my duties in the best interests of shareholders and investors," he stated.
Mr Rambourg had been the co-manager of two of Gartmore's largest hedge funds, but was reassigned to work as an investment analyst following allegations he was directing orders on buying and selling stock from favored brokers.
Gartmore's assets under management dropped five per cent during April 2010 as the internal investigation took place, reported Bloomberg.
By Claire Archer