Gary Vanhoeck, 51, who was originally from Grimsby, was at home on his boat when he was “accosted” by two men, the Royal Bahamas Police Force said.
The intruders, armed with handguns, demanded cash before firing at Mr Vanhoeck and fleeing on foot at around 10pm on May 1.
The victim was pronounced dead at the scene.
Police said they are searching for four men in connection with the incident, which took place at Stuart’s Cove in western New Providence.
A Foreign Office spokesman said: “We can confirm the death of a British national in the Bahamas. We are providing the family with consular assistance at this very difficult time.”
Mr Vanhoeck reportedly quit his job in the UK to move to the Bahamas with his wife a number of years ago, where he became a driving instructor.
He had described their life as: “Living like pirates, diving in the Caribbean.”