Rwanda is the most improved sub-Saharan nation according to a survey looking at performances over the past five years.
Rwanda is recovering from a devastating genocide in 1994
The Ibrahim Index, financed by Sudanese mobile phone magnate Mo Ibrahim, names Mauritius as the best-governed and Somalia as the worst-governed state.
Harvard University academics analysed the criteria used to rank countries.
The Mo Ibrahim Foundation is next month due to award over $5m to a former African head of state who is judged to have demonstrated exemplary leadership.
The presidential prize is also aimed at encouraging best practice.
They assembled data from various sources including the United Nations, the anti-corruption watchdog Transparency International, and thinktanks such as Freedom House.
Countries are measured under categories like "Safety and Security" and "Human Development".
When these categories are put together an overall ranking is reached.
Launching the index, Mr Ibrahim said the aim was to provide an objective assessment of what life was like for ordinary men and women.
"The aim is not to shame or to name anybody. It is really just a snapshot, a photographic shot of what the situation is on the ground, and that in itself is valuable, I think," he said.
Correspondents say some may be surprised by Rwanda's ranking - it came 18th on the list of 48 and had improved by 18 places over five years.
Human rights organisations often portray Rwanda as a state in which the opposition is repressed and journalists harassed and intimidated.
Two island nations top the list of the best governed, Mauritius (Number 1) and Seychelles (2).
Both are stable, relatively wealthy tourist destinations which have little in common with mainland Africa except for the fact that they are members of the African Union.
The BBC's Word Affairs correspondent Mark Doyle says the next batch of countries on the best-governed list are more typical of the bulk of African states.
Botswana, at Number 3, is a stable democracy that earns its money from diamonds and agriculture.
Cape Verde (4) is a former Portuguese colony which survives economically from remittances by expatriate Cape Verdeans - there are said to be more Cape Verdeans in Boston, Massachusetts, than there are on the islands themselves.
South Africa (5), Ghana (8) and Senegal (9) are all vibrant democracies that are proud to have politically well-informed populations.
Worst-governed, according to the list is Somalia, a country which has not had a functioning government since the overthrow of the dictator Siad Barre in 1991.
Other countries scoring badly include Democratic Republic of Congo (47), Chad (46) and Mo Ibrahim's home state of Sudan (45).
Remarkably, Zimbabwe and Equatorial Guinea are better ranked than Nigeria.
Merits of prize
A spokesman for the Mo Ibrahim foundation said there was no automatic link between the "best governed country" index and the "best former president".
Mo Ibrahim has launched the index to combat corruption in Africa
The $5m prize to be awarded on 22 October will be given to an ex-president as a personal retirement gift to be paid in annual tranches and a further sum of $200,000 per annum "may be granted" by the foundation for "good causes espoused by the winner".
Our correspondent says one keen observer of the African scene said granting such a large sum of money to an individual was "scandalous" and that all of it should go to causes like ending poverty on the continent.
Others said the prize had to be substantial to have any realistic prospect of actually encouraging good governance while in office - and that the $5m would spark a valuable debate in civil society about what it means to run a country well.
Nelson Mandela, a towering political figure who would almost certainly have won the prize had he retired within the stipulated 2004-2006 time-frame, said:
"This is an African initiative celebrating the successes of new African leadership. It sets an example that the rest of the world can emulate. We call for leaders across the world - in government, civil society and business - to endorse its aims and back its vision."