I have been scrolling through your answers here, and I don't seem to find any Ugandan company. Sadly, I'm here in Uganda, but I don't have outstanding examples. However, I think we need to define your yardstick for "successful". What I know for sure is that there a a few developers around, but I don't have very good examples of "ground-breaking" software projects accomplished. Well, for purposes of this question, I know WebERP Africa whose accounting system is said to be on Sourceforge (I saw on their website), as well as ClinicMaster (the developer is @Kutegz on Twitter).
I need to specify however that I can't spell out that these match your requirements for "successful".