Central midfielder Sidwell was one of Fulham's best players this season, featuring in every single Premier League match and scoring seven goals.
The 31-year-old - who initially joined Fulham on loan from Aston Villa in January 2011 - was unable to prevent Fulham dropping to the second tier of English football for the first time since 2001 though.
He is not the only big name to leave Craven Cottage, with winger Duff ending his five-year association with the club.
Duff - a member of Fulham's team that reached the 2010 UEFA Europa League final - scored 22 goals in 173 matches for Fulham, but had not featured since February due to injuries.
Elsewhere, full-back John Arne Riise has departed, while experienced midfield pair Giorgos Karagounis and Mahamadou Diarra will not receive new deals.
Centre-back John Heitinga made 14 appearances since signing a short-term deal from Everton in January, but will not have his contract extended, while midfielder Derek Boateng, full-back Matthew Briggs and goalkeeper Neil Etheridge will also leave the club.
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