Makelele said: "The squad Chelsea have put together is one of the best in the world - nobody can doubt that. They are in the hunt for everything in England and in Europe. Already they have a more balanced team than Arsenal and Manchester United, especially in midfield."
The Frenchman believes Chelsea can be better than Real Madrid this season and can go on to dominate European football in the coming years.
Chelsea brought to an end the biggest spending spree the game has ever seen yesterday morning when they confirmed Makelele as their final summer signing.
He said: "Chelsea can be superior to Real Madrid in this very campaign. We can be a better team than them.
"Chelsea will play more as a unit. Madrid base their team around certain players.
"I didn't just opt for this project because of the money, I reckon Chelsea may dominate European football in the coming years.
"I have already enjoyed that experience in Spain and it would be marvellous to repeat it here."
Hernan Crespo, Chelsea's new Argentinian striker, hailed Makelele's arrival. He said: "I have seen Claude on TV and know what a great player he is."