His music combines elements of traditional Ugandan music and Western music. He is best known for his first string quartet, which was included by the Kronos Quartet on their 1992 CD Pieces of Africa, which contains music by seven African composers. His music has also been performed by the Imani Winds.
Tamusuza was born in Kibisi. His early training was in Baganda traditional music. His early instructors included the Reverend Anthony Okelo and Kevin Volans at Queen's University Belfast in Belfast, Northern Ireland. He received his doctorate in composition at Northwestern University, where he studied with Alan Stout.