It also said it planned to invest $100 over five years in the port development.
Georgia's senior government officials told Reuters about a deal early this month, although there had been no confirmation from APM Terminals or RAKIA.
"The port ... is ideally located to become a future hub for Central Asia trade," APM said in a statement.
"We expect to invest $100 million over the next five years."
APM did not say how much it paid for the stake.
Poti is the largest port in Georgia, handling liquid and dry bulk as well as containers. It has 15 berths with a total length of 2,900 metres and more than 20 quay cranes.
The new owner has set up a joint venture with RAKIA, which still owns 20 percent of the port, to operate it.
Poti is APM Terminals' first Black Sea port. Before the purchase its nearest terminal to Georgia was in Italy.
RAKIA bought Poti port and 300 hectares of land in 2008 to develop a free industrial zone. It initially acquired a 51 percent stake and land for $90 million in 2008 and bought the remaining 49 percent for $65 million in 2009. (Reuters)
