The vote came after the union accused tram management of harsh and unjust disciplinary action against employees.
It said staff were being subjected to a hostile and bullying management culture, including victimisation, suspensions and dismissals.
Unite regional officer Lyn Turner welcomed the ballot result and warned that if the strike action went ahead it was likely to take place in the run-up to Christmas and to New Year including New Years Eve.
It would be the first strike action to hit Edinburghs trams since they started running in May 2014.
But Mr Turner said he hoped talks between the union and tram bosses would lead to a resolution of the dispute before that.
The ballot had an 88.9 per cent turnout, with 69.6 per cent voting in favour of a strike and 30.4 per cent against.
We are currently in talks with management and are hopeful that we can come to a sensible agreement which fully addresses our members concerns and avoids the need to take action.
Unite does not want to play Scrooge by interrupting Christmas travel for Edinburghs citizens, but we need management to recognise that our members have legitimate concerns that must be addressed.
We have met with senior management for the last two weeks, discussions have been progressing and we hope management see sense so all this can be put to bed and the drivers can get back to what they do best – driving trams.
Almost 70 per cent of Unite members who took part backed industrial action over concerns staff have been subjected to a hostile and aggressive culture.