The local authority had abandoned plans for the rise after the Scottish government made it clear it would lose far more money than it had anticipated.
Moray's ruling independent/Conservative administration had argued a rise would help avoid cuts in services.
Councillors backed the budget proposals which included raising the cost of school dinners and music tuition fees.
Council leader Stewart Cree said the budget would maintain services for the next year, but there could be some issues in future years.
The Scottish government had made it plain any council that put up the council tax would lose more government funding than before.
This made Moray's plans unrealistic, so council officials came up with other options.
Many other councils across Scotland are continuing to examine possible cuts and savings options.
All 32 local authorities accepted the Scottish government's funding deal.
Moray Council - which had proposed increasing council tax by 18% - has set its budget for the coming year.