The workers were employees of the French aid agency Action Against Hunger (ACF).
There had been reports and rumours that the staff had been killed in the battered town of Mutur.
The Consortium for Humanitarian Agencies (CHA), the main umbrella body for aid agencies in the country, said that one of the relief teams that reached the town had found the corpses in an aid agency office.
The 11 men and four women, all wearing ACF T-shirts, were found face down in their office in Muttur, Jeevan Thiagarajah, the head CHA said.
He said: "They found them in the office on the ground, lying face down - executed."
Thiagarajah said it was not clear who had killed them.
French diplomats in Colombo ruled out the possibility of any of their nationals being among the dead, saying there were no French aid workers in the Trincomalee area.
Mutur has seen days of fighting between the government and Tamil Tiger rebels.
Reporters and photographers who tried to enter Muttur on Sunday were turned away by security forces, although the military took a group of journalists on a conducted tour under tight security on Saturday evening.