The oil and gas operator said exploratory drilling indicated an "estimated 450-550 million barrels of oil equivalent (mmboe)" in the Pecan field, 166 kilometres (100 miles) off Takaradi.
Further exploration could increase total volumes to 600-1,000 mmboe, the company said in a statement.
Ghana's government said the announcement was "good news" that could bring "a new outlook to the economy" and alternative funding for social projects in the future.
Aker Energy began operating the Pecan field last year. It holds a 50 percent stake. Others include Russian energy firm Lukoil and the Ghana National Petroleum Corporation.
Ghana first discovered oil in 2007 and became a producer in 2010, helping to speed up the rate of economic growth. It is believed to have five to seven billion barrels in reserves.
The resolution of a long-standing maritime boundary dispute between Ghana and neighbouring Ivory Coast sparked predictions the country would see an oil boom.
President Nana Akufo-Addo said the favourable ruling opened up "possibilities of development, progress and prosperity", which would help boost funding for schools, hospitals and roads.