More than 100 supporters gathered outside the Royal Courts of Justice ahead of the hearing on Wednesday.
Speaking outside the court, Platon Loizou, Rich Loizou's father, said he and his wife had not attended their son's trial.
"What he actually said to me was, 'Dad, if I go down I don't want to see your face so please don't come up'.
"It was the hardest thing in the world. When we got the call, 15 months, we were shocked."
Loizou's mother Sharon said she thought the courts "wanted to make an example of them to stop other demonstrators. I think it's that simple".
Mr Loizou said his son had committed "no violence, no criminal damage, no intimidation". He added: "This is the thin end of the wedge."
Mrs Loizou said: "I think it's backfired massively. I think it's made ordinary people think this is wrong, we shouldn't be allowing it."
Mr Loizou agreed, pointing out that many of the supporters were "grey-haired people who are saying no for the sake of our children, for the sake of out grandchildren". He added: "We have got to stop this. This is going to destroy the planet, this is a disaster."
Soil scientist Simon Blevins, 26, from Sheffield, teacher Richard Roberts, 36, of London, and piano restorer Rich Loizou, 32, from Devon, had their jail terms quashed and replaced with conditional discharges.
The Lord Chief Justice Lord Burnett said: "We have concluded that an immediate custodial sentence in the case of these appellants was manifestly excessive.
"In our judgment the appropriate sentence which should have been imposed on September 26 was a community order with a significant requirement of unpaid work.
"But these appellants have been in prison for six weeks.
"As a result, and only for that reason, we have concluded that the appropriate sentence now is a conditional discharge for two years."
The judge said the court would give full reasons for its ruling at a later date.
The packed courtroom erupted with applause and some supporters began singing after the decision was announced.
Actress Emma Thompson, who is also an environmental activist, said: "When a government behaves contrary to science, reason and public opinion, it's inevitable that some brave souls will resist.
"I'm truly grateful to the three activists for doing what we should all be doing - trying to protect our children's future from fossil-fuelled disaster.
"Thank God the courts have seen sense and freed them!"
After the ruling, Platon Loizou, father of one of the three, said: "We are just delighted. Today justice has really been done.
"We should not be here in the first place, but what's done is done. We have now got to concentrate our efforts on stopping fracking in this country.
"It is the wrong thing to do and we should never have been doing it in the first place."
John Sauven, executive director of Greenpeace UK, said: "Today's ruling is a major cause for celebration not just for activists, but for everyone whose home, community and climate are threatened by reckless industrialisation.
"Britain's justice system has long recognised the vital contribution peaceful protest makes in a democracy, and we thank the High Court for upholding that principle.
"This is still a country where dissent is tolerated and speech is free."
Mr Loizou added: "This will not change Rich's mind. Richie and the rest of the boys, from what I know, will continue to do this and continue to tell the whole world about what we are doing to ourselves.
"This is supposed to be GB Green Week - it is absolutely ridiculous."
Michelle Easton, partner of Richard Roberts, said she and others would be going straight to Euston to catch the next train to Preston to "go and pick our boys up".
She added: "It is still a conviction but it is within the rights that we have in this country. We don't lock up protesters who are peaceful."
Friends of the Earth lawyer Katie de Kauwe said: "Friends of the Earth intervened in this important case on the basis that these sentences were disproportionate.
"We are very pleased that the Court of Appeal has today found that the custodial sentences were manifestly excessive and quashed them.
"This is a great outcome. The court thanked Friends of the Earth for its intervention and we are awaiting their full reasoning."
Rosalind Blevins, mother of Simon Blevins, said: "I would like to say a huge thank you to the many thousands of supporters, friends, strangers, academics, politicians, trade unions who condemned the original harsh sentence and cried out for the right to peaceful protest.
"Personally, it has meant so much to us families to have your support and belief in us.
"In our euphoria in the moment that the sentence has been quashed, we must not forget what brought us to this place. A protest - one of many years of protesting - against fracking, not only in Lancashire but elsewhere."
Ms Blevins added: "We are all in this together, the citizens of planet earth, and we have to act now. We can make this change if we all pull together."
Ms Easton read a statement on behalf of the three: "Today's decision affirms that when people peacefully break the law out of a moral obligation to prevent things such as the fossil fuel industry they should not be sent to prison.
"The fracking industry threatens to industrialise our beautiful countryside. It will cause famine, flooding and many other disasters on the world's most vulnerable communities by exacerbating climate change.
"Fracking is beginning right now, so there has never been a more crucial moment to take action. Your planet needs you.
"We encourage everyone who is able to join us this Saturday for a mass demonstration at the UK's first fracking site and to look up the activist network Reclaim the Power and find opportunity to take direct action or to volunteer in vital support roles."
Liberty's head of legal casework Emma Norton said: "This is a victory for human rights and civil liberties.
"Civil disobedience plays a vital role in safeguarding our democracy and we are delighted the Court of Appeal has recognised and protected the rights of these protesters, who should never have been in prison."