The jury found the sexual activity was consensual.
Family and loved ones of the defendants clutched hands as they sat in the gallery awaiting the verdict.
As the foreperson of the jury read out the verdicts, the complainant, who sat in the gallery with family and friends, broke down crying.
Tears were also shed by the defendants' loved ones, and one juror appeared to be crying as well.
The complainant's father said their family was "shattered" by the verdict and "very disappointed in the justice system".
"I certainly think that there's got to be a dramatic change in the justice system," he said.
He said the family was "very proud" of their daughter.
"[Our daughter] is a very bubbly, well-liked girl, with one of the best personalities you could every come across. For the last two years there just been a little chunk of that missing."
During the trial, crown prosecutor Megan Jaquiery argued the complainant said no repeatedly before and during the sexual activity, and that she only complied out of fear that something worse might happen to her.
Mr Galvin was represented by Chris Tennet, and Mr Cook was represented by Roger Crowley and junior counsel Jamie Waugh.Mr Crowley and Mr Tennet, both said the sexual activity stopped as soon as the complainant told the men she wanted to go home.
Mr Crowley pointed to text messages sent from Mr Galvin to Mr Cook shortly after the incident, saying "better get her name and number so I can come up and we can do that again."
"Those exchanges demonstrate that both those boys thought what happened in the Unimog was consensual," Mr Crowley said.
"Does it offend your common sense that two men who have just sexually assaulted a young woman are talking about getting her number and doing it again?"
The defence argued the complainant was consenting, but regretted her decision later and made the complaint to quash rumours.
Mr Tennet said after the verdict was read that the case was "an awful thing for everybody".
"Obviously I'm pleased but, you know, it's not nice for the lawyers."
Judge David Cameron called the case a "difficult and a sad one" and thanked the jury for their willingness to continue on into Saturday.