Pictures and video of him in a Gunners shirt was posted on Twitter before the move was officially confirmed by both clubs.
Havertz has joined the north London club in a £65million deal after three years at Chelsea.
The 24-year-old played 139 times for the Blues, memorably scoring the winner in the Champions League final against Man City in 2021.
The Germany international shared his frustration with how the move managed to get out online.
Havertz wrote on Twitter: "Dear Chelsea FC, I would have preferred for you to hear my thoughts on leaving Chelsea first from myself before my thoughts on me joining my new team.
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"This isn't my style and it upsets me that you had to hear of it in this way. I write this letter with a heavy heart to all the fans. A big thank you for all your support, we achieved a dream of winning the Champions League together! Kai."
He then shared a separate statement that read: "Today, I find myself at a crossroads, where words can't describe the emotions I'm feeling. It is with a heavy heart that I write this letter, saying goodbye to the club that has become my second home and to the fans who have supported me throughout this amazing journey.
"Together we have experienced the highs and lows, the joys and the heartaches. I want to thank each and every Chelsea supporter, member of staff, coaches and my team-mates for the last years.
"Joining Chelsea three years ago was a big moment in my life and I'm looking back on these years with nothing but pride, gratefulness and lots of sport success.
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"From winning the Champions League in my first season, to winning the Super Cup and the Club World Cup and now saying goodbye. It's been quite a journey that I will never forget.
"Everyone second of my time at Chelsea, I identified with what it means to represent the club on and off the pitch. I hope that everyone remembers me for this. I'm looking back at the memories that last a lifetime. The club will be forever in my heart and I made friends for life.
"It was an honour to be a part of Chelsea history. Thank you, Kai."