Members of the Communication Workers Union (CWU) backed walkouts by 89 per cent on a turnout of 73 per cent of the 110,000 balloted.
It passed the threshold in the Government's controversial Trade Union Act, under which ballots need a 50 per cent turnout for industrial action to go ahead.
Terry Pullinger, the union’s deputy general secretary, said: “This ballot result is hugely significant and demonstrates a strength of feeling that can only be translated as a massive vote of no confidence in the managerial leadership of the Royal Mail Group.
"They have failed and should resign or be sacked.”
He added: “This is a dispute about honour and we refuse to simply stand aside.”
The vote has sparked concerned that that it could take place over the busy Christmas period, with the ballot valid for the next six months.
"For some families, the timing of any strike or work to rule could mean that Christmas is cancelled by this action," says David Jinks head of consumer research from rival parcel firm ParcelHero.
He added: "If industrial action goes into the seasonal period it will have a huge impact.
"Even if the strikes are limited; it will have significant consequences across the industry as other delivery companies try to absorb the extra volumes at this hugely busy period."
Workers Union could walk out on November 24 and 25 to coincide with the “Black Friday” sales when Christmas shopping begin in earnest.
This could cause major disruption at sorting offices and delay the delivery of millions of online bargains.
Union leaders are due to meet on Thursday to decide on action.
“While no decision has been made yet, it is certainly possible it could be on Black Friday because it is a key part of the lead-up to Christmas.”
The union is accusing the company of "unilaterally" closing its defined benefit, or final salary, pension scheme, with new entrants going into an "inferior" scheme which will leave them in "pensioner poverty".
The union is also in dispute over pay and issues such as delivery office closures.
The CWU Postal Executive will meet later this week to determine the next steps in this campaign and any potential strike dates.
A Royal Mail spokesman said: "Since privatisation, Royal Mail has paid £1.4 billion into employees' pensions. In the same period, Royal Mail has paid £800 million in dividends to shareholders, including colleagues."
They added it was "very disappointed" about the planned strike action.
"Royal Mail is committed to further talks as a matter of urgency, to reach agreement with the CWU. There are no grounds for industrial action.
"In 2013, Royal Mail and the CWU committed to the Agenda for Growth (AFG) - a legally binding agreement. Royal Mail has brought to the CWU’s attention the contractual dispute resolution procedures included in the AFG, which both sides are required to follow once instigated.
"They escalate to independent external mediation, which we expect will take close to Christmas to be completed, and may be longer. We believe these dispute resolution procedures must be followed. The union cannot take industrial action until they have been completed.
"Industrial action is damaging for our business. It undermines the trust of our customers. It makes it harder to pay for the great terms and conditions we provide for our employees. National industrial action means the current offer from Royal Mail, including on pensions, will be taken off the table."
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