The so-called Chennai Six have been found not guilty, according to supporters on a social networking page.
They were first jailed in October 2013 on weapons charges while working as security guards on ships to combat piracy in the Indian Ocean.
The British men are Nick Dunn, 31, of Ashington, Northumberland, Billy Irving, 37, from Argyll and Bute, John Armstrong, 30, of Wigton, Cumbria, Nicholas Simpson, 47, of Catterick, North Yorkshire, Ray Tindall, 42, of Chester, and Paul Towers, 54, of Pocklington, East Yorkshire.
All 35 men who were arrested have been cleared and the Facebook post said families were "understandably delighted" at the news.
They will now wait to see when they will be allowed home from India to their families.
The post said: "The Appeal Court has today found all 35 men NOT GUILTY we now wait to hear as and when the men will be allowed home to their families.
"This may take some time whilst the authorities decide whether they agree with the outcome or wish to appeal.
"If they wish to appeal the men might be released from prison but not allowed back to the UK.
"But the families are understandable delighted that finally common sense and justice has prevailed."
The family of Nick Dunn, from Ashington, Northumberland, gathered together as they waited to hear if the news was good.
Sipping champagne, his sister, Lisa, said: "This is the best champagne in the world, it tastes like the best drink.
"The longer it went on, as much as you still have an element of hope, it does dwindle after having so many delays and setbacks.
"But that hasn't happened today and we've had the best news ever.
"It will make all of our Christmases, all of our dreams have come true today."
Mr Dunn's father, Jim, said: "Absolutely fantastic, the best news in the world.
"We haven't been a full family for a long time now. Nick won't fully realise it's over until his feet touch down in Newcastle."
Yvonne McHugh, partner of Billy Irving, told the Press Association she was "over the moon" the men had been acquitted.
She added: "They've all been acquitted, all 35 of them. We are just waiting to hear how soon they'll be home.
"That's the biggest hurdle we faced and all of them have been acquitted."
Although the men have been cleared, Ms McHugh said she would be unable to speak to Mr Irving as he is not yet out of prison and does not have a phone.
She said: "I won't be able to speak to him until he's out of prison, we just want them home as soon as possible.
"I'm absolutely ecstatic and feel proud we've managed to do this after four years."
Theresa May's official spokesman said: "The Government, from the Prime Minister down, has worked hard for over four years to support the men and their families and we share their happiness at the court's decision to give a full acquittal to each of the men.
"We are now working with the Indian authorities to discuss the next steps. We will continue to offer the men and their families consular assistance for as long as it is needed."