The German club will pay an initial £20m to sign the striker, two years after selling him to the Stamford Bridge outfit for £47.5m.
After scoring 23 goals in 89 Chelsea games, Werner fell out with Thomas Tuchel and was pictured arriving in Leipzig on Monday night ahead of his medical.
“Dear Blues, today marks the end of my journey with Chelsea,” he wrote.
“I am incredibly grateful for the time I spent at this special club. At this point I would like to express my appreciation for my teammate, the coaches and staff, and especially for you, the special supporters.
“I felt so much love and support throughout the last two years and I will never forget how you guys stood behind me in good and in challenging times!
“We lifted trophies like the Champions League together and I will always remember the song you wrote and chanted for me.
“I’m already looking forward to hopefully playing at Stamford Bridge again one day!”