The 30-year-old, who cost about four million pounds according to British media, is the latest high-profile player to leave Newcastle after they were relegated from the Premier League in May.
Forward Michael Owen has moved from St James Park to Manchester United while defenders Habib Beye and Sebastien Bassong have joined Aston Villa and Tottenham Hotspur respectively.
"I am happy my move to Fulham has been completed and look forward to joining in with the rest of the squad's training programme immediately in preparation for two important home matches this week," Duff told www.fulhamfc.com.
"Fulham had a fantastic season last year and I know having spoken to the manager (Roy Hodgson) in recent days the club's ambitions are high and I'm looking forward to the challenges."
"I have known Damien for over a decade since he broke into the first team at Blackburn when I was manager, so I'm fully aware of his qualities and I am looking forward to working with him again," Fulham boss Roy Hodgson said.
