Grealish leaves his boyhood club Villa having made 213 appearances and scored 32 goals since making his senior debut in 2014.
"I've been at Aston Villa for 19 years and I've been a fan my whole life," Grealish wrote in a statement. "I've come through the ranks and captained the club back to the top tier of English football.
"It's impossible to put my feelings into words, but I'll try. When I first came to Villa I had my own personal dreams and ambitions like getting into the first team, scoring my first goal and scoring the winner in a derby. It wasn't until we got relegated that I felt a greater sense of purpose.
"Every time I put on the Villa shirt, I played with my heart on my sleeve. Being given the armband was both a privilege and an honour for me and my family and I've loved every minute of it.
"I want to thank the manager and my teammates, I'll never forget everything we achieved together... and to the fans who supported me through everything, I can't thank you enough.
"To all my coaches and all the people who work at the club behind the scenes who have done so much for me over the years -- thank you.
"I'll always be a Villa fan -- I love this club with all my heart and I hope you understand my reasons for seeking a new challenge. The club are in great hands, the manager, the lads, the news signings coming in -- it's an exciting time to be a Villa fan. I'll see you all again soon. Until next time."
It will be the second time City have held the British transfer record, joining the arrival of Robinho from Real Madrid in 2008.
Speaking to City TV, Grealish added: "There's obviously a lot of reasons why I decided to come here, obviously the manager has been a massive factor in that. Playing under the best manager in the world was something I couldn't really turn down.
"Competing for major trophies is something that I wanted to do, and it was something that, in the end, I couldn't turn down."
Sources have told ESPN that Villa offered Grealish, their captain, a vastly improved deal to stay at Villa Park but that the 25-year-old has chosen to join City because of the lure of top trophies and regular Champions League football.
City first proposed a deal including £90m in transfer fees and winger Morgan Rogers -- who is valued at £10m -- but a straight cash offer of £100m has triggered a release clause in Grealish's contract.
Kane wants to move to the Etihad, but Spurs are privately adamant he is not for sale. Sources have told ESPN that City believe they can finance deals for Grealish and Kane this summer through player sales.
City have raised £109m through sales since the start of the pandemic and could raise another £50m this summer, even without a first-team player leaving.