The 26-year-old Netherlands midfielder will set City back around £46 million and he joins Guardiola's ranks on a five-year deal until 2030.
Reijnders follows midfielder Rayan Cherki, left-back Rayan Ait-Nouri and goalkeeper Marcus Bettinelli through the door ahead of this summer's Club World Cup.
"I am ecstatic to be signing for Manchester City," Reijnders told the club's official website.
"City are one of the biggest teams in the world, with the best coach, world-class players and outstanding facilities.
"Under Pep Guardiola, City have won so many titles and I want to help keep that going with a lot more success in the coming years.
"It is also a dream come true to play in the Premier League. This league has seen many of the best Dutch players perform through the years and it's an inspiration to follow in their footsteps.
"I'm a box-to-box midfielder who likes to join the build-up from the back. I like to help the attackers, create chances and try to score a goal by myself sometimes.
"As a midfielder, it's important to score goals as well. Two years ago, I didn't score that many goals and I worked on it that summer and seeing what I needed to do better in front of the goal. This season, it worked out and I got on the scoresheet more."
Reijnders scored 15 goals across all competitions for AC Milan last season and was named the Serie A's best midfielder.
He has been capped 22 times by the Netherlands and was a substitute for their 8-0 demolition of Malta on Tuesday.
City's director of football Hugo Viana added: "He arrives here with extensive top-level experience in Europe, both at club level as well as on the international stage with the Netherlands.
"Tijjani adds extra energy, composure and creativity to our midfield and working with Pep and our coaches will only see him go from strength to strength."