The boats, seized along with their crews by Iranian Revolutionary Guards last June in the Shatt al-Arab waterway which divides southwestern Iran from Iraq, were included in an exhibition of memorabilia from Iran's 1980-1988 war with Iraq.
They were displayed on the Shatt al-Arab close to where they were captured, IRNA said. An officer at the site will explain to visitors how the boats and their eight crew were seized.
The crew, who Britain said had been delivering the boats to Iraqi police when captured, were held for three days and paraded blindfolded on Iranian television before being released.
London reacted angrily on Friday to Iran's plans to include the boats in the exhibition, which will run over Iran's New Year holiday period until 4 April.
"This is not a constructive way to resolve this dispute," a British Foreign Office spokesman said in London, adding that talks were continuing for the vessels to be returned.
"We are making a formal protest," he said.
Tehran says the boats had strayed into Iranian waters. Britain says they were intercepted in Iraqi waters and forced over to the Iranian border.