Mogae will also receive $200,000 every year for the rest of his life.
Botswana, which has a population of around two million and is the world's biggest diamond producer, is widely regarded as a rare political and economic success story in a continent plagued by corruption and poverty.
"President Mogae's outstanding leadership has ensured Botswana's continued stablility and prosperity in the face of an HIV/Aids pandemic which threatened the future of his county and his people," Annan said.
"Botswana demonstrates how a country with natural resources can promote sustainable development with good governance, in a continent where too often mineral wealth has become a curse."
Tackling corruption
The award was established by Mo Ibrahim, a Sudanese-born telecommunications entrepreneur, as a way of encouraging good governance and tackling corruption.
The winner is chosen by a prize committee of six people, chaired by Annan and including fellow Nobel peace laureates Martti Ahtisaari, a former president of Finland, and Mohamed ElBaradei, the director-general of the International Atomic Energy Agency.
To qualify, nominees must be an African leader who has left power in the last three years.
Mogae stepped down in April this year after almost a decade as president, handing power to his successor Seretse Khama Ian Kharma - the son of Botswana's first president, Seretse Kharma.
Botswana is expected to hold a general election in October next year.
Mogae was previously the head of Botswana's central bank and introduced widespread changes to the economy, encouraging companies to begin coal-mining and opening the country to tourists.
Union opposition
While dramatically increasing spending on the fight against Aids, Mogae made enemies among unionists over his reluctance to raise government spending across the board.
However, he defended the policy in one of his last addresses to parliament saying: "The road to political expediency and populism may be lined with cheering crowds, but in the end, we cannot escape the cold hard facts of our limitations as a developing country.
"As sure as the merry-maker must account for his excesses with a splitting hangover the morning after, an even harsher punishment awaits a nation that spends unwisely in pursuit of immediate gratification rather than sustainable development."
Mogae is only the second leader to win the award, which was established last year.
Joaquim Chissano, former president of Mozambique, was the first winner after standing aside after successfully guiding his country out of years of civil war.