Teams of up to six men will help repair headstones which have been vandalised or have fallen over, as part of a government programme preparing them for release.
It provides long-term prisoners, who are nearing the end of their sentences, access to work to get them ready for life back in the community.
Earlier this year, the city council was approached by the Scottish Prison Service asking if a programme could be set up to allow inmates to work in city cemeteries.
The council gets a "significant" number of complaints from the public about the condition of memorials in graveyards.
But land and environmental boss Brian Devlin admitted there is presently a limited inspection and maintenance programme.
He said: "There a significant number of memorials which have fallen over or been subjected to vandalism and any repair works are currently beyond current resources.
"It is clear there is scope to introduce this programme in the cemeteries, specifically to deal with fallen memorials."
The work carried out by prisoners will include assessing the condition of headstones, turning over or laying flat memorials which have fallen over and uprighting others if possible.
Mr Devlin said: "This is not work which is carried out as a core function by Glasgow City Council staff at present."
Prisoners, who will not be paid, will be supervised by council workers with additional support from prison staff.
Mr Devlin said: "A trial of this programme will be conducted at one of the council's older cemeteries, where there have been no recent burials."
A council spokesman said: "A number of memorials have fallen over or been vandalised and this will help us to carry out improvements while teaching prisoners new skills."