Mateo Kovacic joins Man City from Chelsea on four-year-deal
No financial details were disclosed but British media reported that City paid Chelsea 25 million pounds plus five million in add-ons for the midfielder.
"This is a brilliant move for me, and I cannot wait to get started with City," Kovacic said in a club statement.
"Anyone who has watched this team under (coach) Pep (Guardiola) knows how good they are – for me, they are the best in the world. The trophies they have won are clear for all to see, but they are also the best footballing side out there.
"To be joining this squad really is a dream for any footballer. I still have plenty of learning and developing to do, and I know under Pep's management I can become a better player."
Kovacic began his senior career with Dinamo Zagreb before signing for Inter Milan in January 2013. He made the switch to Real in the summer of 2015.
Kovacic made his Croatia debut in a World Cup qualifier against Serbia in March 2013 and has gone on to earn nearly 100 caps for his country, helping Croatia to the runners-up spot at the 2018 World Cup in Russia and a third-placed finish in 2022 in Qatar.
"Mateo is an excellent footballer," City's Director of Football Txiki Begiristain said.
"He can play as a 6 or an 8, has plenty of experience at top level clubs and he understands the Premier League. It was a very simple decision to bring him to City because he has the tactical and technical qualities we are looking for in a midfielder.
"He is someone we have monitored for a very long time and always we were impressed whenever we watched him.
"I am delighted he is here. This is a great signing for this club, and I am very excited to watch what he can do with Pep and the rest of our backroom team."
Kovacic is City's first signing since the club lifted the FA Cup and Premier League title before completing a rare treble by also winning the Champions League.