The university said it needed to make changes "to remain a world class organisation".
A three-hour meeting of the Senate on Tuesday finally approved the plan by a majority vote.
The Classics Department is to close, despite a last minute plea from the Nobel Laureate, Seamus Heaney, who said it was "a retrograde step which would deprive students of access to the heritage stored in the classical languages".
The demise of the department means Latin and Greek will no longer be available to students in the province.
The subjects have been taught at Queen's since 1849.
Local schools that teach these subjects are said to be angry that their pupils will have to leave Northern Ireland to do a degree in the classics.
Despite claims that demand for the subjects is low, it is understood the number of students has actually risen over the last year.
Research funding
However, the university has defended the closure and other measures including proposed redundancies of staff who are not producing enough good research, and a controversial restructuring of the prestigious Institute of Irish Studies.
If they produce the savings needed, more than 80 new academics can be employed.
The vice chancellor said the plan would enhance Queen's international reputation and it had been shown in the past that tough decisions can pay off.
The university is unhappy it did not get extra research funding to reward its good performance in the last review of departments.
The news follows reports last month that up to four departments at the university were under threat.