Iranian spokesman Ali Rabiei said the vessel "can leave and decisions [made by the judiciary] suggest the seizure has ended."
The Stena Impero was held at the port of Bandar Abbas in the Persian Gulf.
"We have no further information about it," President and CEO of Stena Bulk Erik Hanell told CNN.
The tanker has a British flag but is owned by a Swedish company. It seven Indian crew members were released earlier this month.
Johnson and Rouhani are scheduled to meet on the sidelines of the United Nations General Assembly in New York City, which begins Tuesday.
The Stena Impero was seized by Iran's Revolutionary Guard on July 19 for alleged maritime violations. It followed Britain's seizure of an Iranian supertanker, the Grace 1, in Gibraltar two weeks earlier.
British intelligence has blamed Tehran for drone attacks on two oil-producing areas of Saudi Arabia a week ago. Johnson has said he intends to de-escalate tensions with Iran in his meeting with Rouhani.
"The U.K. is attributing responsibility with a very high degree of probability to Iran for the [drone] attacks," he said. "We think it is very likely indeed that Iran was indeed responsible."