British officials late Wednesday night said they expected Iran to make good on its promise to release 15 British sailors and marines, and hoped their journey back to London would begin "within hours."
The British Foreign Office, meanwhile, confirmed that its ambassador to Iran had visited with the military personnel and reported that they were in good health.
Prime Minister Tony Blair welcomed the announcement Wednesday by Iranian President Mahmoud Ahmadinejad that the 15 troops seized 13 days ago would be freed and said that he bore "no ill will" toward the Iranian people.
Ahmadinejad's surprise announcement came at a news conference shortly after he pinned a medal on the chest of the Iranian coast guard commander who intercepted the sailors and marines.
"On the occasion of the birthday of the great prophet (Muhammad) ... and for the occasion of the passing of Christ, I say the Islamic Republic government and the Iranian people — with all powers and legal right to put the soldiers on trial — forgave those 15," he said, referring to the Muslim prophet's birthday on March 30 and the Easter holiday.
"This pardon is a gift to the British people," he said.
In response to a reporter's question, Ahmadinejad said the Britons would be freed upon the completion of the press conference. Iranian state television said the captives would leave Tehran on a plane Thursday.
The release ends a 13-day standoff between London and Tehran that was sparked when the crew was seized as it searched for smugglers off the Iraqi coast. Britain denied Iranian claims the crew had entered Iranian waters.
"I'm glad that our 15 service personnel have been released and I know their release will come as a relief not just to them but to their families," Blair said outside his No. 10 Downing St. office. "Throughout, we have taken a measured approach, firm but calm, not negotiating but not confronting, either."
Blair added, "To the Iranian people, I would simply say this: We bear you no ill will."
President Bush, who had condemned the seizure of the Britons and referred to them as "hostages," also welcomed it, said his national security spokesman, Gordon Johndroe.
A State Department official said to FOX News, "We are cautiously optimistic — but it ain't a done deal 'til they're out of Iranian airspace, just like the American hostages [in 1981]."
Blair thanked British allies in Europe, the U.N. Security Council and in the Middle East for their help in securing the freedom of the Royal Navy personnel.
• BRAINROOM: Timeline of Events in British Hostage Crisis
Syria's information and foreign ministers said Damascus had played a key role in resolving the standoff.
"Syria exercised a sort of quiet diplomacy to solve this problem and encourage dialogue between the two parties," Foreign Minister Walid al-Moallem said.
After Ahmadinejad's news conference, state television showed him meeting with the British crew, who were dressed in business suits, outside the presidential palace. He shook hands and chatted with them through a translator, and a caption to the video said the meeting was taking place as part of the "process of release."
"We appreciate it. Your people have been really kind to us, and we appreciate it very much," one of the crew could be heard telling Ahmadinejad in English.
Another said: "We are grateful for your forgiveness."
Ahmadinejad responded in Farsi, "You are welcome."
Among the crew at the palace was sailor Faye Turney, the sole woman among the captives, wearing a blue jacket and floral-patterned blue and white headscarf.
Iranian TV said the British captives had watched Ahmadinejad's news conference live and were ecstatic when a translator told them what the president had said.
Three of the 15 captives were shown on Iran's state IRIB 2 television channel thanking Ahmadinejad for freeing them.
Lieutenant Felix Carman was the first to speak, though it was not clear exactly when the interviews were filmed
Carman said the crew's Iranian captors had shown the sailors a "great deal of respect and dignity."
Leading Seaman Faye Turney, the sole woman in the crew, said they were treated well but that "it would be nice to get back, get home and see my family."
Royal Marine Captain Chris Air said the Iranians treated the British service members "very well, with respect for all our rights."
Recent days saw talk of direct negotiations between Britain and Iran, and a decrease in tensions that had risen after Iran broadcast videos in which Turney and the others "confessed" to violating Iranian territorial waters, and Britain expressed outrage.
Ahmadinejad said the British government had sent a letter to the Iranian Foreign Ministry pledging that entering Iranian waters "will not happen again."
The British Foreign Office responded: "We haven't gone into detail of what was in the note. But we have said all along we made our position clear (about being in Iraqi waters)."
Ahmadinejad's announcement came after Iran's state media reported that an Iranian envoy would be allowed to meet five Iranians detained by U.S. forces in northern Iraq. Another Iranian diplomat, separately seized two months ago by uniformed gunmen in Iraq, was released and returned Tuesday to Tehran.
Ahmadinejad said Iran will never accept trespassing in its territorial waters.
"On behalf of the great Iranian people, I want to thank the Iranian coast guard who courageously defended and captured those who violated their territorial waters," he said in awarding a medal to the coast guard commander.
"We are sorry that British troops remain in Iraq and their sailors are being arrested in Iran," Ahmadinejad said.
Ahmadinejad asked Blair not to "punish" the crew for confessing that they had been in Iranian waters when they were seized by Iranian coast guard. Iran broadcast video of some of the crew giving confessions, angering Britain.
He also criticized Britain for deploying Turney in the Gulf, pointing out that she is a woman with a child.
"How can you justify seeing a mother away from her home, her children? Why don't they respect family values in the West?" he asked of the British government.
Iran has denied it seized the Britons to force the release of Iranians held in Iraq, and Britain has steadfastly insisted it would not negotiate for the sailors' freedom.
Iran's official Islamic Republic News Agency said earlier Wednesday that an Iranian envoy would be allowed to meet with the five detained Iranians in Iraq but gave no further details.
A U.S. military spokesman in Baghdad said, however, that American authorities were still considering the request. The spokesman, Maj. Gen. William C. Caldwell, said an international Red Cross team, including one Iranian, had visited the prisoners but he did not say when.
FOX News' James Rosen and the Associated Press contributed to this report.