In August, Targett came close to penning a similar deal with Newcastle United before the move fell through, and the left-back has been restricted to just two Premier League appearances this season.
However, the 22-year-old has been given permission to spend the remainder of the campaign on loan with the Cottagers in the Championship.
Targett told the club's official website: "I'm really happy to be here. I am looking forward to helping the side push on to the playoffs.
"One of the main reasons I joined is that the club is in a great place at the moment and the results have been fantastic. I can't wait to be a part of that.
"I am very excited to make my Fulham debut and the most important thing is that we pick up the three points when I do."
Targett could feature when Fulham face Barnsley on Saturday afternoon.