Gary Vanhoeck was shot on Friday night by two men carrying handguns, police said.
Mr Vanhoeck, 51, was at home on his boat when the shooting took place, reportedly in front of his wife.
The intruders demanded cash before firing at Mr Vanhoeck and fleeing on foot at around 10pm. He was pronounced dead at the scene.
A security guard was reportedly tied up by two men while others boarded the boat, which was moored in front of the scuba diving centre where Mr Vanhoeck worked.
Police said they are searching for four men in connection with the incident, which took place at Stuart’s Cove in western New Providence.
The Bahamas tourism minister, Obie Wilchcombe, told a local paper he was concerned crime was “ruining” the “wonderful reputation” of the islands.
“Right now there is just too much hate and violence and too many individuals churning the crime,” he told Tribune242.
The paper cited a statement from Mr Vanhoeck’s boss that appeared to confirm his killing during an attempted robbery.
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.”