A total of 94 per cent of RMT’s members on the London Underground backed more action - but only 52 per cent bothered to vote.
RMT general secretary Mick Lynch said: "I congratulate every Tube worker in this long running dispute over jobs, conditions and pensions.
"It is an impressive feat for any set of workers to return a 3rd strike ballot in favour of more action and continuing to try to bring this dispute to a negotiated settlement.
"We urge London Underground and the Mayor of London to sit down with the union urgently so we can bring this dispute to a resolution.
"If a resolution cannot be found, we will continue our industrial campaign for as long as it takes to get justice for our people."
No new strike dates have been announced but the union said action would follow if a negotiated settlement could not be achieved.
The RMT said the vote had surpassed the 40 per cent threshold needed for action, as 49.2 per cent of all those entitled to vote supported strike action.
A total of 9,843 RMT members were entitled to vote but only 5,126 took part.
Of those 5,126, a total of 4,827 voted in favour of taking strike action and 269 voted against. Ten papers were spoiled.
The RMT has already held six one-day strikes on the Underground since March, most recently on November 10, in protest at the axing of up to 600 station posts and the perceived threat to staff pensions.
The Tube dispute – which is not about pay – is separate to the action by the RMT and other unions on the national railways, which will effectively be shut down for most of next week, with only about 20 per cent of trains running.
The renewed mandate enables the RMT to go on strike for another six months.
By law, the RMT has to give Transport for London two weeks’ notice of any action – meaning further walkouts could be co-ordinated with action it is taking over Christmas against Network Rail or the round of rail strikes planned for early January.
Aslef, which represents the vast majority of Tube drivers, is also seeking to renew its strike mandate.
Andy Lord, TfL’s interim commissioner, told the TfL board on Wednesday that new station staffing rosters were being introduced but no proposals had been made to change pensions.
TfL has been forced to review its pension scheme as a condition of the Government bailouts but “no change” remains an option. The station staffing changes are being introduced to save cash as TfL battle stop break even by next summer.
Mr Lord said: “We haven’t presented any proposals on pensions. We have complied with the terms of the funding agreement. So, frankly, the industrial action that has been taken is completely pointless, from my perspective.
“We continue to work with the RMT to say it’s really not worthwhile taking industrial action for that issue.”
TfL has warned that the train strikes will also impact on parts of the Tube where tracks are shared with the national railways, such as on the District and Bakerloo lines, as well as the London Overground and Elizabeth Line.
Glynn Barton, TfL’s chief operating officer, said on Thursday evening: "We were notified today that RMT members have voted to renew their mandate for industrial action over jobs, pensions and conditions.
“There are no proposals to change pensions or terms and conditions and we have committed to ensuring that everyone who wants a job will still have a job, in line with our non-compulsory redundancy agreement. We will continue to work with the RMT on these issues.”
Mayor Sadiq Khan said he was concerned at the economic impact of the strikes on West End businesses during the crucial “golden quarter” around Christmas.
Strikes are also planned by nurses, paramedics, firefighters, civil servants, Royal Mail staff, National Highways workers and Border Force guards at six airports including Heathrow and Gatwick – with airlines reportedly having to cancel up to 30 per cent of flights.