British Royal Marines seized the tanker in Gibraltar in July on suspicion that it was carrying oil to Syria, a close ally of Iran, in violation of European Union sanctions. That triggered a series of events that have heightened tensions on international oil shipping routes through the Gulf.
"The vessel is expected to leave tonight," envoy Hamid Baeidinejad said on Twitter, adding that two engineering teams had been flown to Gibraltar.
The Grace 1's detention ended last week, but on Friday a federal court in Washington issued a warrant for the seizure of the tanker, the oil it carries and nearly $1 million.
Gibraltar said on Sunday it could not comply with that request because it was bound by EU law.
"The EU sanctions regime against Iran – which is applicable in Gibraltar - is much narrower than that applicable in the US," the government said in a statement.
"The Gibraltar Central Authority is unable to seek an Order of the Supreme Court of Gibraltar to provide the restraining assistance required by the United States of America."
Washington had attempted to detain the Grace 1 on the grounds that it had links to Iran's Islamic Revolutionary Guard Corps (IRGC), which it has designated a terrorist organisation.
Iran has denied the tanker was ever headed to Syria.
Tehran said it was ready to dispatch its naval fleet to escort the tanker - now renamed the 'Adrian Darya-1' - if required.
"The era of hit and run is over ... if top authorities ask the navy, we are ready to escort out tanker Adrian," Iran's navy commander, Rear Admiral Hossein Khanzadi was quoted as saying by Mehr news agency.
On Sunday, video footage and photographs showed the tanker flying the red, green and white flag of Iran and bearing its new name, painted in white, on the hull. Its previous name, 'Grace 1', had been painted over. The vessel's anchor was still down.
The initial impounding of the Grace 1 sparked a diplomatic row that escalated when Tehran seize a British-flagged oil tanker in the Gulf two weeks later. That tanker, the Stena Impero, is still detained.
The two vessels have since become pawns in a bigger game, feeding into wider hostilities since the United States last year pulled out of an international agreement to curb Iran's nuclear programme, and reimposed economic sanctions.
Iran has denounced US efforts to set up an international maritime security coalition in the Gulf and insisted regional countries could protect the strategic waterway and work towards signing a non-aggression pact.
On a trip to Kuwait on Sunday, Iranian Foreign Minister Mohammad Javad Zarif said in a tweet that "Iran's proposal for Regional Dialogue Forum and non-aggression pact trumps reliance on extraneous actors".
Good talks with Kuwaiti Crown Prince & FM. Praying for Emir's speedy recovery.
Stressed that Iran's proposal for Regional Dialogue Forum and non-aggression pact trumps reliance on extraneous actors.
The Grace 1 had originally flown the Panamian flag but Panama's Maritime Authority said in July that the vessel had been de-listed after an alert that indicated the ship had participated in or was linked to terrorism financing.
'The vessel is expected to leave tonight,' envoy Hamid Baeidinejad said on Twitter, adding that two engineering teams had been flown to Gibraltar.