The 31-year-old spent seven years at Elland Road, winning the Championship twice and playing a key role in their first promotion back to the Premier League.
Bamford had one-year remaining on his contract at Leeds but has now reached a “mutual agreement” to leave the club.
“The club became a massive part of my world, and I tried to make you proud by doing the most I could on the pitch and also in the community,” Bamford said in a video released on social media.
“Right now with the way it has come to an end and the way things have been handled recently, it’s all a little bit too raw to reflect on immediately.
“But I think in the years to come I’ll look back at this period of my life with nothing but joy, pride, and be super happy with what I’ve achieved and the fact that I was able to wear this number 9 shirt in front of you guys for this many years.”