Darren Clark poured petrol on the front door of the flat in Fort House, North Forth Street, and set it alight while his ex-girlfriend Evelyn Ross, 20, was inside with her mother Janis Ross, 41, and sister Lisa Triplett, 17.
The High Court in Perth heard how Clark committed the offence shortly after being freed on bail by the High Court in Edinburgh in relation to another offence.
Yesterday the jury found Clark guilty of attempting to murder the three women at the flat on 3 July last year.
He was found guilty of dowsing the front door in petrol before igniting it, causing the fire to take effect and endangering the occupants and trying to murder them.
The jury found him guilty of previously evincing malice and ill-will towards the women, and of being on bail at the time of the murder bid.
The court was told the couple had split up a short time before. They had an argument and Clark threatened to "firebomb" Miss Ross's home.
The court heard the entrance to the flat was set ablaze, but the fire was extinguished before it managed to take hold on the rest of the tower block. After a trial lasting a week, the jury returned a majority guilty verdict against Clark, who was described in court as being unemployed and without a permanent address.
Advocate depute Jonathon Brodie said: "He was on bail at the time of the offence in respect of another matter, where the indictment was subsequently deserted.
"He has three previous convictions for violence. He has a short schedule of previous convictions."
Lord Emslie deferred sentence for background reports.
Counsel for Clark, Susan Duff, said she would provide a full plea in mitigation when the case calls again at the High Court in Falkirk on 25 February.
Clark, who has been remanded in custody since his arrest in July, remained in custody pending sentence.