GM officials said on Sunday they had agreed to pay Fiat €1.55 billion ($2 billion).
A put option is a contract giving the owner the right, but not the obligation, to sell a specified amount of a security, at a fixed price within a certain period.
It becomes more valuable as the price of the security depreciates because the option price would have been fixed at a higher rate.
The Fiat management agreed to the move at an extraordinary meeting of its administrative board in Turin, with Fiat chief Luca Montezemolo declaring himself "relieved" at what would be a positive signal for the troubled company.
GM had agreed to return its 10% Fiat share to the Italians, and the cancellation of two joint ventures for engine and spare parts production.
Fiat workers had threatened to strike and investors had dumped shares earlier in the month in reaction to an announcement that Fiat and GM had failed to mend a contractual squabble.
The bone of contention was an option allowing Fiat to sell its loss-making car manufacturing division to GM.
The Detroit-based automotive giant, which agreed to the put-option while buying a stake in Fiat in 2000, has financial difficulties of its own and had lost interest in buying the company.
GM managers argue that changes made at Fiat meant the put option was no longer valid - but Fiat asserted its view that the put-option was enforceable.