The 35-year-old took to social media to say his goodbyes after a second spell with the club came to end end, with his contract to expire at the end of the month.
He is among 15 professionals who will leave the club, along with captain Ben Mee, James Tarkowski, Phil Bardsley, Dale Stephens and Erik Pieters, and Under 23 players Joel Mumbongo, Richard Nartey, Anthony Glennon, Ethen Vaughan, Sam Unwin, Anthony Gomez Mancini, Calen Gallagher-Allison, Joel Connolly and Harry Allen.
Lennon made 32 appearances last season, scoring twice, after rejoining the club following a season with Kayserispor in the Turkish Süper Lig.
“I wish all associated at Burnley all the very best.
“Great club, enjoyed my time there!
“Looking forward to my next mission, ready to go again!”
Bardsley, whose wife Tanya had already revealed her husband was leaving the club after five years, added: “My time at Burnley is over, I would like to thank all the staff, my team mates and the fans for the last five years, it’s been an absolute pleasure, met some fantastic people and friends for life.
"I would like to wish you all the very best for the future UTC!!!
"I feel fit and excited for my next challenge and look forward to getting back on the pitch!!!”
Bardsley had been expected to link up with good friend Wayne Rooney at Derby County.