England international Phillips, 26, completed his transfer to the Etihad on Monday.
Premier League champions City paid an initial fee of £45m for the defensive midfielder, who was signed to replace Fernandinho.
Phillips is leaving his boyhood club Leeds United, which he has played for since joining their academy aged 14.
Following confirmation of his move to City, Phillips posted a heartfelt letter to Leeds on his Twitter account in which he thanked the club, their fans, current manager Jesse Marsch and former boss Marcelo Bielsa.
“Where do I start? Firstly, I would like to express what a privilege it has been to play for this incredible club. Since my debut at 17, it’s been a journey any boy from Leeds could wish for,” said writes Phillips.
“When I was young I went to watch my very first Leeds game in the ER and from that moment I knew my dream was to put on that white shirt and step out onto that pitch. I would like to thank all the people involved at the club for making Leeds one of the best clubs in the world Every manager I’ve played with has trusted me and taught me everything I know.
Phillips then thanked former manager Bielsa, who brought the club back to the Premier League in 2020 before quitting last season after a series of poor results.
“I can’t mention Leeds without mentioning a special person – Marcelo,” added Phillips.
“The best manager I have ever met. He was a man who brought the club to life, he gave the players and everyone involved with the club the belief that we were good enough to return to the Premier League. after 16. Not only did you give everything to the club, but you also gave me everything I needed to become the person I am today on and off the pitch.
He also thanked current manager Marsch, who guided Leeds to Premier League safety last season following Bielsa’s departure.
“And now to Jesse, what an amazing manager you are, but what an even better person,” Phillips added.
“You came into this club and gave every player confidence and confidence in a very difficult season and that’s what kept us in the league. From the bottom of my heart, thank you.”
Phillips added: “To all my teammates from my debut to my last game, thank you for helping a boy from Leeds achieve his dream. I wish everyone the best for the future and next season.
“Over the past 4 years you and I boys have shared so many memories, from missing the play-offs, to being promoted and then surviving relegation last season. You you’re all an amazing bunch of boys who deserve it all.
Like a proud father. You have earned this chance and I have no doubt that you will deliver as you have always done for us. An incredible player but I’m prouder of the man you’ve become! Never change friends. Take care of him. 🤍 https://t.co/DZ4PtRxniM
— Liam Cooper (@LiamCooper__) July 4, 2022
“And finally, to my family, the fans! I hope you understand my decision and accept that I only want to pursue my dreams and test myself against and with the best teams and players on the planet. As a As a young child, I had so many dreams and I still do… but playing for you is one I will never forget.
You are the best fans in the world.
“Good luck to everyone involved at Leeds United. I love you all and will miss you. Never goodbye. See you soon. WORD!”