The midfielder, who has played over 100 games for the Cottagers over a three-year spell, also offered his thanks to the club via Twitter.
"It saddens me to say my time at Fulham has come to an end. I have enjoyed every moment in the 3 and half years I've spent here," said the 31-year-old.
"I've been so proud every time I pulled the jersey on and I wore it with pride, gave 100% every time and will always look back with great memories of my time at Fulham FC.
"I'd like to thank all the players, staff and managers for helping me along the way. But most of all I'd like to say thank you....all the fans who have been truly magnificent. From my 1st game to my last I've shared your passion.
"I will always have Fulham FC In my heart. Thank you for a special time and I wish you every success. COYW."
Sidwell joined Fulham on a free transfer from Aston Villa in January 2011 and went on to score 17 goals for the London club.
He was one of their best performers last season, but could not prevent them being relegated to the Championship.
He was one of nine players subsequently released by the club, along with Damien Duff, Giorgos Karagounis, Mahamadou Diarra, Derek Boateng, John Arne Riise, Matthew Briggs, Neil Etheridge and John Heitinga.
Sidwell has been linked with a move to a number of Premier League clubs, including QPR, Stoke, West Brom, Hull City and Southampton.