The sailors will be handed over to their respective country in the future hours or early on Wednesday after going through legal processes, the news agency reported.
There is still no official confirmation of the report.
Earlier an armed forces official has said the detained personnel will be freed if it is proven that they harbored no ill-will.
Three British boats with eight crew were seized in the Persian Gulf waters on Monday.
British Foreign Secretary Jack Straw phoned his Iranian counterpart Kamal Kharrazi on Tuesday on the fate of the arrested crew.
Straw called for release of the captured sailors, saying that they had entered the Iranian waters through a minor incident, the press department of the Iranian foreign ministry said.
“After interrogating these people and after we are sure of how this matter happened, we will take the necessary measures,” the statement quoted Kharrazi as saying.
Foreign Ministry Spokesman Hamid-Reza Asefi said on Monday that Iranian military had instructions to detain anybody entering Iranian territory illegally.
Iran's Arabic-language satellite channel Al-Alam said the troops had already "confessed" to having crossed into the Iranian side of the Shatt al-Arab waterway which forms the southern part of the border between Iran and Iraq, according to AFP.
"They were 1,000 meters (yards) inside Iranian territorial waters," the military source was quoted as saying. Al-Alam identified the two officers in the group as Robert Webster and
Thomas Higgins.
Webster told the channel that the team, en route from the Iraqi port of Umm Qasr to the main southern city of Basra, had made a "navigational fault".
The British embassy in Tehran said it was still trying to gain access to the eight, 24 hours after they were detained.
"We are still trying to get access," a spokesman at the embassy,
Andrew Dunn, told AFP.
"We do not know where they are being held," added the diplomat, who said earlier that London -- obviously eager to stop an incident becoming a crisis -- was "hoping for a swift solution to the situation."
Television pictures of the men sitting on sofas inside an office in an undisclosed location, as well as shots of seized weapons and communications equipment, have been shown on Iranian state television.
The men were dressed in T-shirts and combat trousers and had serious expressions, but appeared to be unharmed. Officials said they were taken into custody without a shot being fired.
A Royal Navy spokesman in London said the three small patrol boats were involved in training Iraqi river police.
British armed forces control the Basra region. They patrol, in conjunction with Iraqi security forces, parts of the Shatt al-Arab, mostly to combat smugglers and militants seeking to infiltrate Iraq and fight against the U.S.-led coalition.
In Basra, an official said the Iraqi coastguard was trying to broker negotiations between British forces and Tehran to secure the release of the commandos.
Southern coastguard chief General Ali Hammadi said the British crew was controlling landing stages used by smugglers on the Iraqi side of the Shatt al-Arab, when their boats drifted on to the Iranian side.
According to AFP Tehran's ambassador to London, Morteza Sarmadi, was summoned to
the Foreign Office just hours after Kharrazi told British counterpart that he would personally look into Monday's incident.
"Mr. Sarmadi saw a senior official," a Foreign Office spokesman said. "The ambassador was asked to explain why the eight are being held, for their release as soon as possible and for full consular access to them meanwhile."
"He was asked for information on the reports that they will be prosecuted, and told they were on a routine mission. Our ambassador in Tehran, Richard Dalton, has made the same points to the Iranian ministry of foreign affairs."
MS/IS
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MNA