The British crew sat in business class on the British Airway's flight that departed Mehrabad International Airport around 8:30 a.m. local time, an Associated Press reporter at the scene reported. They were expected to arrive in London around noon local time (7 a.m. EDT).
CBS News correspondent Larry Miller reports that after arriving at Heathrow Airport, military helicopters will take the crew to an Air Force Base to be debriefed on their nearly two weeks in Iranian captivity.
Once airborne, the sailors and marines celebrated their freedom with champagne and laughter, according to a British reporter aboard the flight.
"There's champagne being drunk and lots of laughter on the plane," Sky television correspondent Ian Woods said in a telephone call from the plane.
On board, the 15 were given fresh military uniforms for their arrival at Heathrow Airport, Col. Andy Price of Royal Marines told reporters.
The sailors arrived at the Tehran airport in a convoy of black sedans about an hour earlier escorted by the elite Revolutionary Guards. British ambassador to Iran, Geoffrey Adams, who was at the airport, declined to comment.
Before boarding, they received gifts given to them on Ahmadinejad's behalf including handicrafts, a vase and special Persian sweets, Iran's state-run news agency, IRNA, reported.
The hardline president's announcement of their release Wednesday defused a growing confrontation between the two countries. In London, British Prime Minister Tony Blair expressed "profound relief" over the peaceful end to the 13-day crisis, telling the Iranian people that "we bear you no ill will."
The crisis had raised oil prices and fears of military conflict in the volatile region. The move to release the sailors suggested that Iran's hardline leadership decided it had shown its strength but did not want to push the standoff too far.
Iran did not get the main thing it sought - a public apology for entering Iranian waters. Britain, which said its crew was in Iraqi waters when seized, insists it never offered a quid pro quo, either, instead relying on quiet diplomacy.
Syria, Iran's close ally, said it played a role in winning the release. "Syria exercised a sort of quiet diplomacy to solve this problem and encourage dialogue between the two parties," Syrian Foreign Minister Walid al-Moallem said in Damascus.
Ahmadinejad timed the announcement so as to make a dramatic splash, springing it halfway through a two-hour news conference Wednesday.
The president first gave a medal of honor to the commander of the Iranian coast guards who captured the Britons, and admonished London for sending a mother, Leading Seaman Faye Turney, on such a dangerous mission in the Persian Gulf.
He said the British government was "not brave enough" to admit the crew had been in Iranian waters when it was captured.
Ahmadinejad then declared that even though Iran had the right to put the Britons on trial, he had "pardoned" them to mark the March 30 birthday of the Prophet Muhammad and the coming Easter holiday.
"This pardon is a gift to the British people," he said.
After the news conference, Iranian television showed a beaming Ahmadinejad on the steps of the presidential palace shaking hands with the Britons - some towering over him. The men were decked out in business suits and Turney wore an Islamic head scarf.
"Your people have been really kind to us, and we appreciate it very much," one of the British men told Ahmadinejad in English. Another male service member said: "We are grateful for your forgiveness."
Ahmadinejad responded in Farsi, "You are welcome."
Three members of the crew were later interviewed on Iranian state-run TV, apologizing for the alleged incursion into Iran's waters and again thanking Ahmadinejad for their release.
"I can understand why you're insulted by the intrusion into the waters," said Lt. Felix Carman, shown seated on a couch.
"Thank you for letting us go and we apologize for our actions, but many thanks for having it in your hearts to let us go free," Turney said.
The U.S. cautiously welcomed Iran's announcement, though Vice President Dick Cheney said "it was unfortunate that they were ever taken in the first place."
The British crew was seized March 23 as it searched for smugglers. Iran broadcast footage of Turney and some other crew members "confessing" they had entered Iranian waters. An infuriated Britain froze most bilateral contacts, prompting Tehran to roll back on a pledge to free Turney.
Wednesday's announcement led some analysts to conclude that Iran's supreme leader, Ayatollah Ali Khamenei, decided the crisis had gone on long enough at a time when Tehran faces mounting pressure over its nuclear program. A day after the British were seized, the U.N. Security Council imposed new sanctions on Iran for refusing to halt uranium enrichment.
During Ahmadinejad's news conference, he said Britain had sent a letter to the Iranian Foreign Ministry pledging that entering Iranian waters "will not happen again." Britain's Foreign Office would not give details about the letter but said its position was clear that the detained crew had been in Iraqi waters.
Regardless of the territorial issue, the standoff showed that Tehran has ways to push back after the U.S. and Britain beefed up their military presence in the Persian Gulf this year.
The U.S. has accused Iran of sending weapons to Shiite militias in Iraq. That led to speculation that the Iranians seized the Britons in retaliation for the detention of five Iranians by U.S. forces in the northern Iraqi city of Irbil in January. Iran denied any connection.
Shortly before the announcement, Iranian state media reported that an Iranian envoy would be allowed to meet the five Iranians. A U.S. military spokesman in Baghdad said American authorities were considering the request, although an international Red Cross team, including one Iranian, had visited the prisoners.
Another Iranian diplomat, separately seized two months ago by uniformed gunmen in Iraq, was released and returned Tuesday to Tehran. Iran accused the Americans of abducting him, a charge the U.S. denied.