Two of the men - convicted sex offender Neil Strachan and gay rights campaigner James Rennie - were convicted of sex attacks on children.
Strachan, 41, and Rennie, 38, both from Edinburgh, were also found guilty of conspiring to abuse youngsters, as were three other members of the gang.
And all eight accused in the 10-week trial at the High Court in Edinburgh were convicted of a series of child porn offences.
The gang members were traced through their explicit internet chats about sexual fantasies involving children.
Nearly 125,000 indecent images were seized during Operation Algebra, which uncovered the group, believed to be Scotland's biggest paedophile network.
Ross Webber, 27, of North Berwick, Craig Boath, 24, from Dundee and John Milligan, 40, from Glasgow, were all found guilty of conspiring to participate in the sexual abuse of children along with Strachan and Rennie.
The five men, with Colin Slaven, 23, from Edinburgh and Neil Campbell, 46 and John Murphy, 44, from Glasgow, were also convicted of a catalogue of child porn offences.
The jury - down to 14 men and women after one member was discharged during the trial - took 10 hours over two days to reach its verdicts.
The court fell silent as the succession of verdicts to more than 50 charges were given.
Five men - Strachan, Rennie, Webber, Boath and Milligan - were found guilty of conspiring to get access to a child or children to commit abuse.
From various locations across Scotland, they plotted, whether by using web cameras or other means such as by phone, to participate in sexual offences, including rape and sodomy.
Campbell was also accused of conspiracy, but he was cleared on that charge after the jury found the case against not proven.
Strachan and Rennie faced charges of actually abusing three young victims in this case. Strachan was convicted of attempting to rape an 18-month-old boy in Edinburgh on New Year's Eve in 2005.
The attack was captured in a photograph known in court as The Hogmanay Image. Strachan was also found guilty of repeatedly touching a six-year-old boy indecently on the same night while he was asleep.
The jury found Rennie, the former chief of LGBT Youth Scotland, an organisation dedicated to helping young gay people, guilty of molesting a young boy over more than four years. The child was just three months old when the abuse began.
Rennie was also found guilty of two charges of attempting to defeat the ends of justice by accessing insecure internet connections.
The men were all convicted of a string of child pornography offences. All eight were convicted of possessing and making indecent images and seven of them were found to have distributed images. A charge of distribution against Slaven was withdrawn by the Crown.
All the offences were committed in Edinburgh, Glasgow, Dundee and East Lothian during various periods ranging from February 2004 to May 2008.
The mother of an 18-month-old boy abused by Strachan said today she would never be able to forgive him for the "sick" attacks on her son.
She said in a statement: "The anguish I feel towards Mr Strachan is indescribable.
"I feel that no matter what punishment given to Mr Strachan it will never be able to compensate for the hurt, devastation and great deal of stress brought to me and my family.
"Mr Strachan used and abused our trust in order to satisfy his and others' sick needs."
The family of the baby abused by Rennie said their life had been "turned upside down" since they discovered the close family friend had targeted their son.
"For a year and four months now we have had to live with the impact and haunting consequences this has had on our lives.
"For over 15 years James Rennie seemed the closest of family friends and it is hard to put into words the extent of the betrayal he has exacted upon us, as many of the details may identify our family and son.
"To subsequently learn that he abused our son, and invited others to do the same, has been devastating. As a family we have had to learn to live, and cope with, the effect these horrific events have had."
The convictions come after one of the most complex and challenging investigations yet carried out by Lothian and Borders Police.
The inquiry, which reached around 200 individuals across the world, uncovered what is thought to be Scotland's largest paedophile ring.
Officers, with the help of other partner agencies, recovered thousands of CDs and DVDs, hundreds of computers and thousands of harrowing images of abuse against children - some of which shocked experienced investigators.
The men were brought to trial by Operation Algebra, set up by the force in 2007 after indecent images were found on computer equipment used by Strachan during his work for a paint firm.
During the two-month trial, members of the jury had to look at a selection of disturbing images. They were also told about the content of a succession of graphic online chatroom discussions about underage sex and child abuse.
The trial was told each indecent image in a catalogue of thousands was a record of sexual assault on a real child.
Prosecutor Dorothy Bain told the jury words such as "pornography" and "indecent" masked the "awful truth" contained in the charges against the men.
A central figure in the gang was a man who once worked for an organisation dedicated to helping gay and lesbian youngsters.
The trial heard how former LGBT Youth Scotland boss Rennie allowed an interest in child abuse to "engulf" his life.
The court heard Rennie had links with paedophiles in America and Europe and confessed to police he had looked at pornography with children in it.
Milligan was found to hold a massive catalogue of more than 75,000 images and was responsible for distributing a significant number of them.
Police investigations of Webber's computer uncovered numerous online conversations.
Ms Bain added that there were no words to explain how awful the "indescribable" discussions were.
Other online exchanges showed further depraved discussions between Boath and Milligan.
"What he expressed an interest in would make any decent person feel physically sick," Ms Bain said of Boath.
