Collin Lee, 67, an employee of International Aid Services (IAS) from Bermuda, suffered fatal gunshot wounds in an ambush, Capt Paddy Ankunda, Ugandan army spokesman said on Monday.
The IAS condemned the attack in a statement issued on its website. It said the ambush occurred some 19 km from Kaya, near the town of Morobo. The ambushed vehicle was travelling to Yei.
Ankunda said: "The rebels ambushed their Land Cruiser vehicle setting it ablaze before they abducted Collin and his wife along with their driver."
He added: "Combined forces of SPLA [Sudan People's Liberation Army] and our [Ugandan] army pursued them and as we were about to get to them, they shot them.
"Collin who was shot in the chest died five minutes after we rescued them, but his wife and driver were brought to Arua hospital for treatment and they are recovering."
The 12 LRA fighters involved in the ambush, Ankunda said, had fled towards neighbouring Democratic Republic of Congo.
Aid workers said LRA rebels have recently targeted them.
On 2 November, the Swiss Foundation for Mine Action (FSD) suspended its operations in areas of southern Sudan after the LRA killed two of its de-miners - an Iraqi international team supervisor and his Sudanese colleague.
The FSD said the killings occurred when its convoy of three vehicles travelling from Jebelin minefield to Nasito Campsite, about 30 km south of Juba, was stopped by three armed men.
A week earlier, two aid workers were killed in LRA attacks in northern Uganda, prompting several NGOs to suspend work in the region.
The latest actions by the LRA have come in the wake of last month's indictments issued by the International Criminal Court against several LRA leaders. Some relief agencies believe the indictments are likely to lead to an escalation of the violence.
Tens of thousands of people have been killed and more than 1.5 million displaced in northern Uganda since the LRA started fighting nearly two decades ago.
LRA leader Joseph Kony, who is believed to be hiding in southern Sudan, and his forces have been accused by human rights groups of massive abuses, including the abduction of at least 20,000 children who are used as porters, fighters and sex slaves by LRA commanders.