Relegation-threatened Livorno have sacked Domenico Di Carlo after just 88 days in charge and re-appointed Davide Nicola.
Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
The Cottagers revealed the move for the 21-year-old on their official Twitter feed, with Frimpong also acknowledging it by writing: "Fulham here I come".
Frimpong has been with Arsenal since he was nine but did not make his Premier League debut until August 2011 after a succession of injuries.
Fitness problems also cut short a loan spell with Wolves last season, with Frimpong needing surgery after rupturing knee ligaments against QPR.
He went on loan to Charlton at the end of 2012 and will now see out the season with Martin Jol's men.