And for the first time, staff under 50 will be able to apply for voluntary redundancy,
But department heads will decide which employees will be able to walk away with a deal.
It is understood shedding 300 posts could cost the council around £21million in redundancy payments but result in savings of £12m a year.
Three years ago, the council launched a scheme offering staff over the age of 50 the chance to take early retirement or voluntary redundancy.
A total of 2175 workers have so far left the council with a further 417 due to leave by the end of March next year, saving around £44m
But further budget cuts mean more jobs losses are needed.
Those who choose to take up the new deal and leave through early retiral will get six and two third years added to their pension, plus 30 weeks' early retiral payment or up to 66 weeks' voluntary severance payment.
A report says: "In extending the scheme, the main difference will be that employees, both under and over 50, will be invited to apply to leave the council.
"Employees will be required to leave by March 31, 2013 unless associated service reforms require a later date."
Council leader Gordon Matheson said the job cuts are necessary because of massive budget cuts.
He added: "Extending our early retirement and voluntary severance scheme will save us around £12m a year.
"That is over and above the £44m we are saving every year as a result of the current scheme.
"We have to save £50m over two years and will have some very, very tough decisions to take but this scheme will help us generate some of those savings. It will be repaid within two years, so we are spending to save.
"We have a commitment there will be no compulsory redundancies."
SNP and Green councillors failed in their bid to delay the move to let hundreds more staff leave pending a full review of how previous job losses had hit services.
Green group leader Nina Baker said: "Council services are already suffering because we have let pretty well anyone go who wanted to go.
"We lost some marvellous people.
"Another 300 job loses will make things worse."