The club entered administration in June with debts of about £30million - with Lithuanian firms Ukio Bankas and UBIG due the vast majority of money while also together owning about 80 per cent of the club's shares.
UBIG abstained from the vote staged at Tynecastle on Friday morning but 87 per cent of those taking part did back a £2.5million rescue bid being offered by fans' group Foundation of Hearts.
A shareholders' meeting is also due to take place at 12pm but even if they back the FoH offer, it may be February before the process of taking the club out of administration is complete.
A statement released on the Hearts official Twitter page said: "BREAKING: 87% of creditors vote in favour of CVA. Stage 1 complete, four stages remain in order to complete deal."
- Ukio Bankas