Political parties had been banned from competing in elections for nearly 20 years in order to curb sectarian tensions.
President Yoweri Museveni instituted the non-party "Movement" system of government when he came to power in 1986.
Enthusiasm for the poll was muted, however, as both the government and opposition supported a return to a multiparty system.
Some political groupings, including the Forum for Democratic Change, boycotted the poll, claiming that it would legitimise 19 years of rule by an effective one-party state.
[1] Other observers suggested the $12.5m spent on the referendum might have been put to better use elsewhere in Uganda, one of the poorest countries in the world.