Uganda has started pulling its forces from Central African Republic, which for years had been the base for troops chasing the rebels, military spokesperson Brigadier Richard Karemire said.
The news comes shortly after the United States' decision last month to pull out of the manhunt for Kony, who is wanted by the International Criminal Court, saying the active membership of his Lord's Resistance Army is now less than 100.
At the peak of its powers, the rebel group was known worldwide for its cruelty against civilians in Uganda, Congo, the Central African Republic and what is now South Sudan. In 2012, the US-based advocacy group Invisible Children made a highly successful video highlighting the LRA's alleged crimes, including the abduction of children for use as sex slaves or fighters.
Kony, a former Catholic altar boy whose rebel movement aspired to rule Uganda according to the biblical Ten Commandments, is wanted by the ICC for war crimes and crimes against humanity. One of his former commanders, Dominic Ongwen, is currently on trial at The Hague-based court.
Although the military mission's ultimate goal was to capture or kill Kony, there has been no word on his exact whereabouts for years even as many of his top commanders defected or were killed.
About 1 500 Ugandan troops had been deployed in CAR under an African Union military mission to defeat the LRA. All of the Ugandan troops will return home by the end of May, with the first arriving home on Wednesday, military spokesperson Karemire said.
Uganda's mission to neutralise the LRA "has now been successfully achieved," he said.
Amid concerns about the military pullouts, the African Union last month suggested that United Nations peacekeeping missions in the region be used to continue anti-LRA efforts.
The US first deployed about 100 US special forces as military advisers to the manhunt in 2011, and in 2014 it sent 150 Air Force special operations members and airmen to assist African forces.
The US Africa Command late last month cited the weakening of the LRA for its decision to remove its military forces, though it was not clear when the withdrawal would take effect. Marine General Thomas Waldhauser declared the hunt for Kony largely over, calling the rebel leader "irrelevant" and in survival mode.
At the time, Uganda's military said its troops would not immediately pull out of the mission against the rebel group, with Karemire insisting that Kony will be a cause for concern as long as he is still alive.