The four drones will be part of a $45m (£28m) military aid package aid to the two countries.
Uganda and Burundi contribute the 9,000 peacekeepers to African peace force in Somalia battling Islamists that control much of the country.
The US sees Somalia as an al-Qaeda haven in East Africa.
Air strikes
The US military command for Africa (Africom) confirmed to the BBC that the Pentagon plan was to strengthen Uganda’s and Burundi’s counter-terrorism capabilities.
The military aid is to include body armour, night-vision gear, communications and surveillance systems.
The al-Shabab Islamist group, which has links to al-Qaeda, control large swathes of southern and central Somalia, including parts of the capital, Mogadishu.
Analysts say Somalia’s weak interim government relies heavily on the African Union peacekeepers to stave off the threat posed by al-Shabab.
There have been US air strikes on al-Shabab in the past, and a US special operations team killed Saleh Ali Saleh Nabhan, one of the most senior leaders of al-Qaeda’s East Africa cell, inside Somalia in 2009.
The US has a military base in neighbouring Djibouti where some 3,000 US troops, as well as armour, aircraft and drones are based.
Somalia has been without an effective central government since the fall of Siad Bare in 1991.