The 31-year-old appeared in every league game for the London club last season, scoring seven goals, but was unable to prevent them dropping to the second tier.
Sidwell, who joined Fulham from Aston Villa in January 2011, will now continue his career elsewhere as Fulham rebuild their squad.
"It saddens me to say my time at Fulham has come to an end," he wrote on social networking site Twitter. "I have enjoyed every moment in the 3 and half years I've spent here.
"I've been so proud every time I pulled the jersey on and I wore it with pride, gave 100 percent 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 first 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."
Sidwell is expected to remain in England's top flight, with the likes of QPR, Stoke City and Newcastle United among those linked with his services.