Members of the Educational Institute of Scotland (EIS) last month voted against a deal offering a 9% increase, with a further 3% next year.
The strike ballot was set to begin on Monday as part of the campaign to secure an improved settlement.
A revised pay offer was put forward by the Scottish Government on Thursday, however, with a letter confirming the proposal on Friday, the union said.
The EIS Council has now agreed “overwhelmingly” to recommend teachers accept the fresh deal.
The new offer is for a 3% rise backdated to April last year, 7% from this April and a further 3% from April 2020, the EIS said.
The union said the offer represents “a significant success for Scotland’s teachers” and it has called off the move towards possible strike action.
The Scottish Government welcomed the decision to suspend the ballot on industrial action.
EIS general-secretary Larry Flanagan said the union has been campaigning for action over issues such as the recruitment and retention of teachers, professional development, workload, and the level of support for pupils with additional support needs, as well as pay.
He said: “The new proposed offer outlined in today’s letter from the Scottish Government represents a positive attempt to address these issues.
“It offers a 3-year pay settlement of 3% from April 2018, 7% from April 2019 and 3% from April 2020 for a compounded total increase of 13.51% over three years.
“It also includes additional commitments aimed at tackling workload, supporting teacher professional development, and enhancing the teacher leadership programme.
“Taking all of these elements together, it represents a package that the EIS is now recommending to Scotland’s teachers.”
In October last year, thousands of teachers and their supporters marched through Glasgow as part of their campaign for a larger pay hike.
Responding to the development on Friday, Deputy First Minister and Education Secretary John Swinney said: “I welcome the EIS decision to suspend the ballot on industrial action.
“The Scottish Government and (local government body) Cosla made a strong offer to teachers which, by a narrow margin, was rejected.
“Given the importance we place on valuing teachers and improving the attractiveness of the profession, I have looked again at the investment the Scottish Government is making.”
He added: “This landmark agreement brings together a partnership with local authorities and professional associations to tackle critical issues, in tandem with a settlement on pay.
“It is an agreement that removes the threat of industrial action, will provide the stability we need to make the reform Scotland’s education system needs and deliver the best possible outcomes for our young people.”