Lt Carman was seen on TV pictures broadcast in Iran

Three of the 15 held are from Wales - Lieutenant Felix Carman, from Gower, Andrew Henderson, from Wrexham, and Corporal Dean Harris, from Carmarthen.

The group is expected to be flown home to Britain on Thursday.

Andrew Henderson's uncle said the family was "ecstatic", while Lt Carman's parents described their "disbelief" at the news.

The group had been held in Tehran since 23 March after being accused of straying into Iranian waters, a claim denied by the UK government.

I just fell to the floor and I think Paul burst into tears - it was so totally unexpected Alison Carmen

Iran's president, Mahmoud Ahmadinejad, announced on Wednesday all 15 were being released as a "gift" to Britain.

They are expected to be handed to the British embassy in Tehran on Thursday morning and then flown home.

Lt Carman's parents, Alison and Paul, from Port Eynon, in south Gower, described their shock at hearing the news their son would be released.

Mrs Carman said: "I just fell to the floor and I think Paul burst into tears - it was so totally unexpected.

"We can't express our feelings - disbelief.

"We are so grateful to the Iranian people for giving the gift to us, bringing our Felix back home to us."

Mr Carman added: "[It's been] absolute hell - an emotional roller coaster without the fun.

"At times we thought things were looking a bit better, then they got worse again."

The family of Corp Harris, 24, a Royal Marine from the village of Trevaughan, near Carmarthen, released a statement which said celebrations would be put on hold until it was certain the service personnel were on their way home.

Dean Harris, from Carmarthen, is another of the freed Welsh sailors

The family said: "This is an overwhelming relief to us that they have agreed to free Dean and the rest of them.

"But until we can see he is out of there, either on a plane or somewhere safe, we cannot raise our hopes."

A close friend of Corp Harris, Gareth Owen, said he was delighted at the news.

"I'm just putting the beer on ice for when he comes back," he added.

The family of Andrew Henderson, 24, from Coedpoeth, near Wrexham, said his parents were "absolutely over the moon".

On hearing the news, Andrew Henderson's uncle, Jim Pye, said: "We haven't come to terms with it.

"We're ecstatic - it's been awful."

Mr Pye said Operator Maintainer Henderson's family had "spent 13 days just watching the news".

He added his nephew "wouldn't have had a problem" coping with captivity.