Members of the Communication Workers Union (CWU) backed the action on Tuesday after ballot papers were sent out three weeks ago.
Any strike dates are yet to be decided but the CWU said if a walk out goes ahead, it could amount to the biggest ever action taken by its members.
Royal Mail said it was "disappointed" by the vote.
"In the event of industrial action, we have contingency plans to minimise customer disruption and will work to keep people, businesses and the country connected," a statement said.
The CWU is the latest of several unions to ballot for strikes in recent weeks as the cost of living soars.
Workers on the railways and at airports are also in pay disputes with employers, with prices for goods in the UK rising at the fastest rate in 40 years.
The union said postal workers "will not budge" until they receive a "dignified, proper pay rise".
Responding to a tweet in which Royal Mail said it was "disappointed" at the vote, the CWU tweeted "dry your eyes mate".
Some 97.6% of members from a 77% turnout voted in favour of striking.
The union has demanded Royal Mail group enters into negotiations to secure a "straight, no-strings pay increase for workers".
Dave Ward, CWU general secretary said there will now be a "small window" for talks to avoid walkouts before strike dates are set.
But he said Royal Mail's chief executive and board "should seriously consider their futures" as the ballot was "also a vote of no confidence".
"While bosses rake in £758m in profit and shareholders take £400m, workers are expected to take a serious real-terms pay cut," he added.
"Postal workers won't accept their living standards being hammered by bosses who are typical of business leaders today - overpaid, underqualified, out of their depth."
Royal Mail said it had offered workers a "deal worth up to 5.5% for CWU grade colleagues, the biggest increase we have offered for many years, which the CWU rejected".
"Despite nearly three months of talks, the CWU have not engaged in any meaningful discussion on the changes we need to make to adapt," a statement added.
It is understood that after talks ended between the CWU and Royal Mail, the company announced it would give members a a non-conditional 2% pay increase backdated to 1 April.
The union has been told a 3.5% is available subject to further talks and agreements, which would total a 5.5% rise.
Terry Pullinger, deputy CWU general secretary, said the union wanted negotiations with Royal Mail, but claimed this was "rejected", leaving reps with "no choice but to fight their disgraceful imposition".
Inflation, the rate at which prices rise, hit 9.1% in May and is forecast to go higher later this year.
But while there have been calls for pay rises, there are concerns that higher wages to cope with the current cost of living could fuel further inflation.