The button, aimed at children and teenagers, will report abuse to the Child Exploitation and Online Protection Centre (Ceop) and Facebook.
The application will also appear on their homepage to say that "they are in control online".
The launch follows months of negotiation between Ceop and Facebook, which initially resisted the idea.
Ceop, the government law enforcement agency tasked with tracking down online sex offenders, called for a panic button to be installed on social networking sites last November.
Bebo became the first network to add the button with MySpace following suit, but Facebook resisted the change, saying its own reporting systems were sufficient.
Pressure mounted on Facebook following the rape and murder of 17-year-old Ashleigh Hall by a 33-year-old convicted sex offender, posing as a teenage boy, who she met on Facebook.
Forty-four police chiefs in England, Wales and Scotland, signed a letter backing Ceop's call for a panic button on every Facebook page.
'Reassurance for parents'
The agreement to launch a child safety application is the culmination of months of negotiation between Ceop and Facebook.
Jim Gamble, Ceop's chief executive, said in a statement: "Our dialogue with Facebook about adopting the ClickCeop button is well documented - today however is a good day for child protection.
"By adding this application, Facebook users will have direct access to all the services that sit behind our ClickCeop button which should provide reassurance to every parent with teenagers on the site."
Facebook's head of communications in the UK, Sophy Silver, told BBC News that the new app would integrate reporting into both Facebook and Ceop's systems.
"Both sides are happy of where we have got to," she said.
"We still have the Facebook reporting system and by having a pre-packaged application that users play an active part in, you not only help keep them safe, it makes all of their friends aware too, and acts as a viral awareness campaign.
"Ultimately though, this makes for a safer environment for users and that's the most important part," she added.
In addition to the online reporting application, a new Facebook/Ceop page is being set up, with a range of topics that, it is hoped, will be of interest to teenagers - such as celebrities, music and exams - and will link these subjects to questions about online safety.
BBC News
