"Even without oil, we are doing so well... With oil as a shot in the arm, we're going to fly," he told the BBC.
"My joy is that I'll go down in history as the president under whose watch oil was found to turn the economy of Ghana around for the better," he said.
The discovery of 600m barrels of light oil offshore was announced on Monday.
Reserves in the Mahogany exploration well were far greater than the 250m barrels that UK-based firm Tullow Oil had earlier forecast.
Tullow, which saw its shares rise more than 12% on the news, jointly owns the West Cape block where the drilling took place with Anadarko Petroleum.
Correspondents say champagne bottles were popping at Osu Castle, the seat of Ghana's government, after the announcement.
Mr Kufuor said the discovery would give a major boost to Ghana's economy.
"Oil is money, and we need money to do the schools, the roads, the hospitals. If you find oil, you manage it well, can you complain about that?" he told the BBC's Focus on Africa programme.
He dismissed suggestions that Ghana may follow in the footsteps of other countries that have mismanaged their oil wealth.
"Some are doing it well and I assure you if others failed, Ghana will succeed because this is our destiny to set the good pace for where we are. So we're going to use it well," he said.
"We're going to really zoom, accelerate, and if everything works, which I pray will happen positively, you come back in five years, and you'll see that Ghana truly is the African tiger, in economic terms for development."
His sentiments were echoed in many of Ghana's newspaper headlines on Tuesday.
The Statesman hailed the Gold Coast, Ghana's name under British rule, finding "black gold" and the Accra Daily Mail leads with the headline: "Thank God. Oil at last Thank God!"
The BBC's Will Ross in Ghana says the country is the midst of an energy crisis and every four days everybody has their electricity switched off for more 24 hours.
Ghana is described as somewhat of a success story in Africa but the country does suffer from widespread poverty and also has alarming levels of corruption, our correspondent says.
Tullow chief executive Aidan Heavey said the discovery was one of the biggest oil discoveries in Africa in recent times, but warned it could be up to seven years before the oil started to flow.
Tullow Oil holds a 22.9% stake in the West Cape Three Points licence and just under 50% in the Deepwater Tano licence.
The move comes as foreign firms are increasingly tapping into Africa for oil.