They were convicted of murder and sexual assault in 2009, then acquitted in 2011, then had their convictions upheld in 2014 before being definitively acquitted by the Supreme Court in Rome in 2015.
The controversial case, which generated massive coverage on both sides of the Atlantic, was the subject of a recent Netflix documentary.
The Instagram account contains dozens of photos of her current boyfriend, Christopher Robinson. They started dating last year and moved in together a few months later in Seattle.
They are pictured camping in Jasper National Park in Alberta, Canada, outside the Pantheon in Paris and at home in Seattle with friends and assorted pet cats.
One photo shows a padlock they attached to a bridge in Paris with their initials - AMK (Amanda Marie Knox) and CGR.
Their travels also took them to the D-Day beaches in Normandy, Brittany, Alsace, Stuttgart, Munich, Montana and New York.
In one photo, Knox is wearing a black t-shirt with the image of pair of handcuffs and the words "It could happen to you" - a reference to the four years she spent behind bars in Italy after her arrest.
Another picture shows a collection of books on criminal justice, with titles such as "Women Doing Life", "Prosecution Complex" and "The New Criminal Justice Thinking".
Since her release from jail, Knox has become an advocate for wrongly incarcerated prisoners and the welfare of prison inmates.
The American also dismissed a story which claimed that she had committed suicide and left behind a note confessing to the murder of Kercher. The story, which was entirely fabricated, appeared on a website designed to look like CNN's web page.
"Reports of my death are greatly exaggerated," she wrote on Twitter. The fake story could not be accessed any longer on Wednesday.
Earlier this year Knox wrote a detailed account of how a lesbian inmate tried to seduce her during her years behind bars in Capanne prison in Umbria.
She said the idea of straight women in prison resorting to lesbian relationships "brings out the horny teenage boy in many of us," but argued that sexual bonds were often a reflection of a yearning for companionship in a brutal environment.
The only person to have been convicted of Kercher's murder is Rudy Guede, a petty criminal from Perugia who is serving a 16-year jail sentence.
This story was originally published by The Daily Telegraph.
