The move comes two years after Scotland's finance watchdog advised them to do so.
Councillors will screen severance deals on offer to senior managers after a number of big-ticket payouts over the last two years, some worth hundreds of thousands of pounds.
The move, confirmed today, brings the city into line with guidance from Audit Scotland, the body responsible for making sure taxpayers' money is not wasted.
Glasgow has paid off some 2800 workers since it announced an early retirement package in 2009 – shaving £45million a year off its wages bill.
Those leaving include some of its most senior officials and department directors, individuals entitled to substantial payouts under the scheme.
City SNP leader Graeme Hendry has formally asked Audit Scotland to investigate such exit packages, claiming they may not have been value for money.
Audit Scotland spelled out its guidelines in a special report on the issue "Bye now, Pay Later" in 2003. And in 2010 the watchdog told Glasgow that councillors should become involved in such decisions.
In a report on Glasgow's 2009 early retirement scheme, they said: "There is a risk that members are not able to discuss and agree potentially contentious retirement/redundancy decisions prior to their approval."
Glasgow City Council immediately responded by saying that councillors had approved the local authority's overall redundancy policy and that "in future members will be made aware of redundancy and recruitment costs associated with senior officers."
Today, a council spokesman said councillors would screen any exit package for senior officials under a new round of voluntary redundancies and early retirements announced for the New Year.
He said: "Bye Now, Pay Later recommended members be involved in redundancy and early retirement decisions for senior officers.
"Members did approve our scheme, including the terms of redundancy and early retirement for all grades, in November 2009.
"When Audit Scotland considered our scheme in 2010, it recommended that members should be further involved in future. However, our scheme had already been agreed by members.
"Future schemes will address that recommendation."
Councillor Hendry said: "It would seem clear that Audit Scotland recommended that councillors should be involved in approving voluntary severance for early packages.
"Instead of implementing this, council leader Gordon Matheson has stuck his head in the sand, resulting in millions being spent on voluntary severance packages without any business case to show savings."
Mr Matheson declined to comment.