Nine out of 10 teacher members of the National Education Union (NEU) voted for strike action and the union passed the 50 per cent ballot turnout required by law.
The union has declared seven days of walkouts in February and March, but says individual schools will only be affected by four of the days.
The first day of strikes will be on February 1 and more than 23,000 schools in England and Wales are expected to be affected, the NEU said.
Overall, 300,000 teachers and support staff in England and Wales were asked to vote in the ballot.
Support staff in schools in Wales are also set to go on strike in the dispute over pay after 88 per cent of balloted members backed action, with a turnout of 51 per cent.
However, the NEU’s ballot of support staff in schools and sixth-form colleges in England did not achieve the 50 per cent ballot turnout required by law for action.
Downing Street earlier urged teachers not to strike and inflict “substantial damage” on children’s education.
Prime Minister Rishi Sunak’s official spokesman said: “We would continue to call on teachers not to strike given we know what substantial damage was caused to children’s education during the pandemic and it’s certainly not something we want to see repeated.
“We would hope they would continue to discuss with us their concerns rather than withdraw education from children.”
The wave of industrial action which has swept the country for months will continue this week and could escalate unless there is a breakthrough in bitter disputes over pay, jobs and conditions.
Members of the Royal College of Nursing across England will walk out on Wednesday and Thursday. The union has warned that if progress is not made in negotiations by the end of January the next set of strikes will include all eligible members in England for the first time.
The government continues to insist that pay claims are unaffordable and is sticking to its belief that wage rises should be decided by pay review bodies.
A demonstration will be held outside Downing Street on Monday to mark the second reading in parliament of proposed legislation on providing minimum levels of service during industrial action.
The vote from the NEU, the largest education union in the UK, comes after a ballot of members of the NASUWT teachers’ union last week failed to reach the turnout threshold.
The National Association of Head Teachers is also due to announce its ballot result for strikes on Monday.
The Department for Education has offered a 5 per cent pay rise to most teachers for the current school year, but the NEU is demanding a fully-funded above inflation increase.
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Mary Bousted and Kevin Courtney, joint NEU general secretaries, said: “We have continually raised our concerns with successive education secretaries about teacher and support staff pay, and its funding in schools and colleges, but instead of seeking to resolve the issue they have sat on their hands.
“It is disappointing that the government prefers to talk about yet more draconian anti-strike legislation rather than work with us to address the causes of strike action.”
The union leaders added that historic real-term pay cuts for teachers had created an “unsustainable situation” in the midst of a cost-of-living crisis. Staff were leaving the profession “in droves”, they said.
“This is a scandalous waste of talent and taxpayers’ money yet the government seems unbothered about the conditions they are allowing schools and colleges to slide into,” they said.
Ms Bousted and Mr Courtney added: “It continues to be the aspiration of the NEU and its membership that this dispute can be resolved without recourse to strike action.
“We regret having to take strike action, and are willing to enter into negotiations at any time, any place, but this situation cannot go on.
“We met with Gillian Keegan last week and would be happy to do so again, but no concrete proposals on teacher or support staff pay were put forward.”
On Monday, Ms Keegan told the House of Commons that she plans to meet education union leaders later this week.
The NEU said teachers in sixth-form colleges in England, who have already been balloted and been on strike in recent months, will also take part in action between February 1 and March 16.
Last week, schools across Scotland were shut as members of the Educational Institute of Scotland, NASUWT, Scottish Secondary Teachers’ Association and AHDS took strike action.
Schoolchildren in Scotland will miss more lessons this week as members of the EIS are beginning 16 days of rolling walkouts on Monday.