The event, held at the Independence Grounds in Kampala, will be Museveni’s sixth inauguration as a democratically elected leader.
Museveni was declared winner of the Jan.14 election after defeating opposition candidates.
The event featured parades, inspection of guards, flypast, Ugandan Special Forces display, cultural display, among others.
Presidents who attended the ceremony were those of Democratic Republic of Congo, Kenya, Guinea, Conakry, South Sudan, Namibia, Ghana, Somalia, Zimbabwe, Burundi, Tanzania and Ethiopia.
Other countries represented in official capacity were Sudan, Gabon, South Africa, Equatorial Guinea, Angola, Mozambique, Saharawi Republic, Algeria, Russia, United Arab Emirates, Saudi Arabia, Rwanda, China, Egypt, Zambia, Sri Lanka and Malawi.
The Chairperson of the African Union Commission, Mr Moussa Faki and Dr Peter Makhuki, Secretary-General, East African Community, also graced the event.
Earlier in his address, Museveni harped on Pan-Africanism and the importance of African integration.
He said that economic, and where possible, political integration in Africa, was pivotal in addressing the issue of prosperity and security in the continent.
Osinbajo has departed Kampala for Abuja, Nigeria.