"Iberia and the union representatives of 93 percent of the staff have agreed to accept and implement the proposal of the mediator Gregorio Tudela with respect to the viability plan for the company," it said in a statement.
Ground and flight staff had threatened to strike from March 18th to 22nd, after two similar strikes that caused thousands of flights to be cancelled, in protest at plans to cut 3,800 jobs.
But the airline said that strike would be called off after workers accepted proposals to reduce the number of jobs cuts to 3,100, improve the severance payments and lighten salary cuts.
The striking workers had denounced the restructuring plan by International Airlines Group, the holding company set up for Iberia and British Airways, after the two merged in 2011.
They accused IAG of trying to dismantle the pride of Spanish civil aviation for the benefit of BA.
Iberia executives say the airline accumulated €850 million ($1.1 billion) in losses between 2008 and September 2012.
In a bid to stem the red ink, the Spanish airline plans to slash its network capacity by 15 percent and downsize its fleet by 25 aircraft, including five long-haul jets, by the middle of this year.