The Teachers' Union of Ireland has voted overwhelmingly to support the revised offer on payments for supervision and substitution.
The TUI voted by 87 per cent to 13 per cent to accept the €37 per hour offer.
Last night, Mr Jim Dorney, general secretary of the TUI, said the result was a "vindication of the negotiating process". The TUI executive had urged members to accept the deal.
Mr Michael Moriarty of the Irish Vocational Education Association said the result would be welcomed by school managers and seen as a resounding vote for common sense.
The main terms of the revised offer included:
• €37 per hour for supervision and substitution duties;
• a back-payment of up to €1,270;
• an offer to examine the pensionability of all supervision payments.
Earlier this year, the TUI rejected the original supervision offer of €34 per hour.
The TUI's strong support for the new deal could create difficulties for the ASTI, whose members withdrew from supervision duties in March. The ASTI has refused to negotiate until its pay demand for 30 per cent is resolved. ASTI members, however, work alongside TUI members in over 120 schools, mostly community and comprehensive schools.
The Government's contingency plan is thought to have cost in excess of €15 million since the ASTI ban on supervision began in March.
Meanwhile, the ASTI president, Ms Catherine Fitzpatrick, has launched an inquiry into leaks from the union's standing committee. In a letter sent to members, she said such leaks were damaging to the interests of the union.