The 43-year-old Dubliner was the general manager of the luxury Silks Hotel on the island and had been living there for the past nine months.
The killing happened on Sunday night during a long bank holiday weekend on the island.
A three-man gang brutally attacked the Irishman after he tried to stop them robbing his friends Rick and Alicia Davison in a raid at the Pagua Bay House in the village of Marigot.
The couple are the owners of the guesthouse and Mr Costello was visiting them as the robbery took place.
When he intervened, one of the gang struck him on the head with a large curved sword known as a cutlass.
The blow to his head caused horrific injuries and he died shortly afterwards.
The gang escaped with a number of possessions belonging to the victims, including mobile phones.
The couple were taken to hospital, where they were undergoing treatment.
Police spokesman Claude Weekes confirmed that the killing had taken place, but full details of the horrific attack have not yet been released.
A local woman told the Herald today that the Irishman's death had shocked the island of 70,000 inhabitants.
Jordan Jermaine, whose family employed the Irishman to run their luxury hotel, said Joe had "died a hero".
He paid tribute to the Irishman as a great man who was very nice and very sociable. Everyone liked him and his death had caused deep upset in the community, he said.
The Dubliner had frequently spoken of his happiness at working on the paradise island.
Dominica is known to have the most unspoilt and spectacularly beautiful environment in the region.