The facility, which will cremate up to five bodies a day when fully operational, is to be built in Cork harbour.
Cork County Council yesterday gave permission to Strikemount Ltd for the development at Rocky Island, formerly used by Irish Steel as a storage depot.
A spokesman for the company said there was very strong demand for the service in the south of the country, currently only available at Glasnevin, Newlands Cross or Mount Jerome.
He said the distance relatives had to travel only added to their distress.
In addition, families living in the south of the country have to pay hundreds of euros to take the bodies of their relatives to Dublin crematoria.
About 20% of funerals in Dublin involve cremation, compared to less than 5% in Cork, where there is no crematorium.
On the continent the figures are far higher, with 72% choosing cremation in Britain, 71% in France and 48% in Holland.
“We expect that when the option becomes available in the South of Ireland the demand will also grow,” the spokesman said.
The crematorium will be built around the remaining building on Rocky Island and will incorporate a spiritual area, family rooms and rest rooms. The company also intends to restore the island, which it said was in a poor condition due to its former industrial use.
Rocky Island became a gunpowder store for the British navy in 1808. It remained unoccupied from the 1920s to 1964, when it was taken over by Irish Steel which built a bridge connecting it to Ringaskiddy.
Cork county manager Maurice Moloney said the council had spent some time looking at the application and was satisfied that all issues surrounding it had been dealt with.