Members of the Association of Teachers and Lecturers have voted to back the Government's revised pensions deal. Some 91.6 per cent of ATL members voted in favour of the deal, thrashed out after a one-day strike in November with six other teaching unions.
ATL is one of the smaller, more moderate unions and represents 160,000 teachers, heads, lecturers and support staff.
Its president, Alice Robinson, said her union's members were "realists".
Their decision was followed by an announcement that secondary school heads were also backing the deal. Leaders at the Association of School and College Leaders (ASCL) said they were accepting it despite "huge anger" over the way negotiations had been conducted.
A third union, the National Association of Head Teachers, failed to approve the deal. But it agreed to continue negotiations "in good faith and without further industrial action".
A spokesman for the Department for Education welcomed the decisions of the ATL and ASCL.
Ministers are hoping the ATL withdrawal of the threat of strike action will put pressure on the two biggest teachers' unions – the National Union of Teachers and the National Association of Schoolmasters Union of Women Teachers – to follow suit.