The strike, which the Unite union said could ground "as many as 35 airlines", had been due to take place over 4-7 May.
However, the action was pulled on Monday (29 April) after affected Unite members accepted new and improved pay and conditions.
Airlines that had been at risk of disruption included Virgin Atlantic, Delta Air Lines, Emirates and Air France.
A spokesperson for Aviation Fuel Services said: "We are pleased to confirm the planned industrial action involving AFS from 4-7 May has now been cancelled and normal service will go ahead."