John Harbor said the money was delivered on Friday morning. He said he expects the pirates to release the crew and leave the ship within about 24 hours, after counting the money.
The ransom amount was not specified.
The chemical tanker Pramoni was hijacked on January 1 in the Gulf of Aden.
The crew includes 17 Indonesians, five Chinese, one Vietnamese and one Nigerian.
Somali pirates have made tens of millions of dollars over the past two years hijacking ships for ransom.
Multinational naval forces have stopped many attacks near the coast, but pirates have increasingly focused their efforts on the Indian Ocean, an area too large for foreign navies to effectively patrol.
An EU naval force spokesman says ransom has been paid for the release of a Singapore-flagged chemical tanker, held for nearly two months by Somali pirates.