Up to 750,000 public sector workers will hold a co-ordinated strike later this month after members of a third major union backed industrial action.
The PCS said its 290,000 members had to defend themselves against "attacks" on their pensions by the government.
But ministers called it "irresponsible" and said the 32.4% turnout showed the strike had "extremely limited support".
The civil servants will walk out on 30 June - the same days as hundreds of thousands of teachers and lecturers.
The National Union of Teachers and the Association of Teachers and Lecturers have announced a nationwide walkout, affecting thousands of schools in England and Wales.
Alongside action from PCS members - who include court staff and immigration officers - it will be the biggest outbreak of industrial unrest in the public sector for many years.
Labour leader Ed Miliband wrote on Twitter: "Strikes are a sign of failure on both sides. Government needs to get round table not ramp up rhetoric."
The PCS said 61.1% of those balloted voted in favour of strike action, while 83.6% backed action short of a strike.
General secretary Mark Serwotka said every person in the country would feel the effects of the strikes - and the month-long overtime ban that will follow.
"Schools will be shut, jobcentres will be closed, driving licences wont be issued, queues will form at ports and airports," he said.
Mr Serwotka said civil servants were being asked to work up to eight years longer and accept a three-fold rise in their contributions, while also seeing their eventual payments halved.
"It's absolute daylight robbery.
"I don't think it's surprising that people will want to defend themselves and if you're going to defend yourselves it obviously makes sense that you make common cause with council workers, health workers and teachers because we all face the same attacks."
Mr Serwotka accused Cabinet Secretary Francis Maude of "deliberately trying to mislead people" about the size of an average public sector pension.
Mr Maude said a worker on the median salary of £23,000 would have a pension pot of £500,000 - equivalent to about £15,000 a year - after 40 years' service.
But Mr Serwotka said the true average for low paid staff was £4,200 a year - "a poverty pension" - and Mr Maude's figures were based on an unreasonable life expectancy of 105 years.
Further talks between the government and union leaders are scheduled for 27 June, but Mr Serwotka said negotiations so far had been "a farce".
"There is no indication whatsoever that the government is having any second thoughts," he said. "What they've told us is at every meeting is that they will not compromise."
He said he believed this would be the first co-ordinated strike of many, with anything up to four million workers potentially walking out in October if nothing was done.
The largest civil service union, Unison, has already said it is also "going down the road to industrial action", and following the PCS vote, the Prison Officers Association said every one of its UK branches would hold protest meetings on 30 June as an act of solidarity.
Brendan Barber, leader of the TUC, told the BBC he was "going to see what happens with the talks" before deciding on the next step to take.
An independent review of pensions by former Labour minister Lord Hutton put the average at between £5,600 and £7,800 a year.
However, that figure takes into account everyone to whom a pension is being paid, regardless of whether they have spent 40 years working in the public sector or just a few months.
Someone who spends their entire working life in the public sector could expect to retire on a pension of two-thirds their final salary.
Mr Maude told the BBC it was "totally irresponsible" for Mr Serwotka to call a strike at this stage in the negotiations.
"It's totally premature and actually his members have rumbled him because in this ballot less than one out of every five of his members voted for strike action," he said.
The minister said there had been "a great deal of progress" so far in the talks and it was "simply not true" to say that the government was not interested in compromise.
He insisted it was fair to ask public sector workers to pay "a bit more" for their pensions - with an average rise in contributions of 3% - given that life expectancies were increasing and taxpayers were feeling the squeeze elsewhere.
And he added: "We continue to hope that industrial action will not take place, but in the unfortunate event that it does we can assure the public now that all services have highly developed and rigorous contingency plans."
London Mayor Boris Johnson and business organisation the CBI have suggested there should be a minimum turnout for union ballots in favour of strike action.
Earlier this month, Business Secretary Vince Cable said that while the case for changing the law was currently "not compelling", if there were co-ordinated and damaging strikes, "the pressure on us to act would ratchet up".
Mr Maude said he agreed with Mr Cable about the possibility of new legislation, adding: "We don't think the case is made at the moment, but we haven't ruled it out."
Mr Serwotka said the turnout would have been much higher if unions were allowed to use modern methods, such as online voting, to carry out their ballots and there were no calls from politicians for minimum thresholds in other kinds of election.
Lord Hutton's review rejected any suggestion that public sector pensions were "gold-plated", but said that in order to make them affordable for the future, millions of employees should work longer, receive less and have their pensions linked to career average earnings, rather than final salaries.