The men were arrested for trying to leave Turkey with a cargo of T-shirts with allegedly false documents as part of an alleged export fraud.
They left for Istanbul yesterday after a court ordered their release from a jail in Edirne, north-west Turkey. They are expected to fly home today.
The Turkish public prosecutor Hayati Onder said there was insufficient evidence to keep them in custody but they would have return to Turkey next month for the next court session.
Graham Quinn, 44, and Tony Quinn, 43, both from Bradford but not related, and Peter Thomas, 46, from Bristol were held following their arrest last November.
Ralph Davies, owner of Cheltenham-based haulage firm for which the three worked, said: 'It's great news and I'm thrilled for their families. They were always 100 per cent innocent.
'It can't have been much of a Christmas for them but now they can come home and celebrate new year.
'Our problem is just beginning though - we need to find a way of getting back pounds 250,000 worth of trucks from Turkey. I don't think that will be easy.'
Mrs Maureen Quinn, wife of Tony, of Bierley, Bradford, was in court to see them freed. She ran from the court to telephone Mrs Jane O'Shea, Mr Thomas's granddaughter.
Mrs O'Shea, of Bedminster, near Bristol, said yesterday: 'We're thrilled to bits by the news. It is brilliant. It has not yet sunk in. We are all so overwhelmed.
'It's what we've all been praying for. When he comes home we're going to have a few drinks and celebrate in style - we can't wait to have him back home. All three of them were in a terrible state and the charges were completely false.
'They should not have been in prison in the first place.
She claimed the Turkish authorities had no right to throw them into prison and described the conditions they were kept in as 'terrible'. 'They were in a tiny freezing cell with mould growing out of the walls. They haven't even been able to change their clothes.'
'It's the best Christmas present we could have wished for. We cannot wait to get them back on British soil.' She said the men were travelling immediately to Istanbul before flying home.
Flight arrangements had not yet been fixed but a family party of about 14 would go to London to meet them.
Graham Quinn's wife had also flown out to Turkey. Mrs Joan Sagar, Mr Quinn's mother-in-law, said: 'We knew they were innocent and it is a tremendous relief. It has all been so unnecessary.
'We knew Graham would never get involved in anything illegal.
'The whole thing has been a nightmare. When they get back we will celebrate a late Christmas and have a great party.'
She added: 'It has been a sad Christmas for all of us.'
A Foreign Office spokesman in London said the men had originally hoped to return from Turkey with a cargo of fruit, but eventually set off with a consignment of T-shirts instead.
They had been detained in the border town of Ipsala by customs police.
At the border their documentation appeared to show more cargo than was in the lorry, which would illegally qualify them for export incentives, he said.
The court also ordered the release of one of three Turks indicted in the case, but said Halil Yildiz, the owner of the trading company, and Ali Celik, a customs official, would remain in custody.
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