Article:The club had asked its main creditors, which include the council, to write off about 70% of its debts.
Cabinet members discussed the proposal on Thursday.
The council said the redevelopment of the Swalec Stadium was part-funded by loans from creditors including themselves, with £16m owed.
Glamorgan asked creditors to write-off 70% of the money and interest owing and agree to a restructuring of the remaining 30%.
The plan to write off £4.4m from a debt of £6.4m the club owes to the council was recommended in a report to the council's cabinet.
Councillor and cabinet member Graham Hinchey said: "As with many organisations, changes to the economy had a detrimental effect on Glamorgan County Cricket Club.
"However, it is imperative that this long established sporting institution does not go into administration."
Glamorgan chief executive Hugh Morris said: "The council's decision is extremely important to the club and is one of the final pieces in the jigsaw in re-negotiating our debt.
"The club still faces financial challenges in the months and years ahead and we are mindful of our responsibility to develop our business to safeguard our long-term future."
Glamorgan's other main creditors - Allied Irish Bank and Paul Russell - the club's former chairman, have also agreed to the restructuring proposal.
The club successfully hosted an Ashes Test at the Swalec Stadium with Australia in 2009 and will host a further Ashes Test this year.

A summary of the above article is?
A £4.4m debt owed by Glamorgan Cricket Club has been written off by Cardiff council.