Collin Lee, 67, and his three-months-pregnant wife were driving from Uganda to the Sudanese town of Yei on Saturday when they were attacked about 12 km (7 miles) from the border.
"Collin was shot in the chest and died in Yei," said Onesimo Yugusuk, operations director in southern Sudan for International Aid Services. "His wife is in shock, but she was not hurt."
The rebels, who are largely based in the lawless mountains of south Sudan, began attacking aid workers last month for the first time in their 19-year-old war against Uganda's government.
Two Ugandans working for international humanitarian agencies were killed in separate ambushes in northern Uganda on October 26.
Five days later two men, a Sudanese and an Iraqi working for a Swiss-based mine-clearing organisation, were shot dead in an attack on their convoy near the southern Sudanese town of Juba.
Experts on the conflict say the rebels appear to have started attacking foreigners in response to an October 14 statement by the International Criminal Court that it had issued its first arrest warrants for the LRA leadership.
Speaking by telephone from the Ugandan capital, Yugusuk said Lee's body was brought to Kampala on Sunday and arrangements were being made to send it to his family home in Bermuda.
"Their driver was shot in the hand and is being treated in hospital. We believe this was the LRA," Yugusuk told Reuters.
Led by self-styled mystic Joseph Kony, the LRA insurgency has uprooted more than 1.6 million people in northern Uganda and triggered one of the world's worst humanitarian emergencies.
The cult-like group has never given a clear account of its political aims, but it is notorious for massacring civilians, mutilating survivors and kidnapping more than 20,000 children who are forced to serve as fighters, porters and sex slaves.