After his visit to Uganda, he will go to South Africa for the 10th Brazil, Russia, India, China and South Africa (BRICS) Summit.
Mr Modi is expected to hold discussions on bilateral relations, including signing of memoranda of understanding (MoUs) in areas of cooperation between Uganda and India.
The Minister of Foreign affairs minister Sam Kutesa who received the Indian premier says top on the agenda will be talks about machinery, medicine and energy.
It is the first state visit to Uganda by a sitting Indian prime minister in 21 years.
After bilateral talks with President Museveni at State House Entebbe, Mr Modi will later in the evening address and engage the Indian community in Uganda at Kololo Independence Grounds.
Mr Modi, who has just left Rwanda is visiting Africa for the second time.
His first visit was in July 2016 when he visited Mozambique, Tanzania, Kenya and South Africa, on a charm offensive mission to counter efforts by other Asian powers, particularly China.
Earlier in 2015, Mr Modi convened the India-Africa summit, the third of its kind, in New Dehli to strengthen ties with African countries.
The summit was attended by some 19 African heads of State, including President Museveni.
Mr Museveni has visited India thrice — in 1992, 2008 and 2015 — in official capacity, and four times in private capacity.
In 2017, Indian vice president Mohammad Hamid Ansari visited Uganda and donated medical supplies — drugs and equipment worth $3b (Shs10b).
In April this year, President Museveni and Mr Modi met briefly on the sidelines of the Commonwealth Heads of Government Meeting in London.