New Real Madrid signing Mateo Kovacic has expressed his delight at joining what he described as the "biggest club in the world".

The Croatian midfielder was handed the number 16 shirt by club president Florentino Perez having joined the Spanish giants from Inter on Tuesday.

The 21 year-old was quick to endear himself to his new employers during the presentation ceremony which took place in the presidential box at the Santiago Bernabeu.

"Many thanks to everyone," Kovacic said. "I'd like to thank the president for his kind words and express my gratitude for the support of the club as a whole.

"I'm at the biggest club in the world and it's very special. 

"I have high hopes for myself and the whole team. Hala Madrid!"

Perez, meanwhile, took the opportunity to welcome Kovacic to the club and outline what was expected of him.

"Being a part of this club is a privilege," Perez said. "One that also brings with it great responsibility, dedication, effort and sacrifice.

"Your country, Croatia, loves football, and you are the fifth Croat to join Real Madrid. 

"This is now your home, this club will be by your side and the fans will support you all the way if you give your all for this badge, as your international team-mate Luka Modric has done. 

"We're sure you're going to help us to keep on improving and that with your talent and dedication, you'll experience something unique; the thrill of going down in Real Madrid's great history. 

"Welcome to your new home, welcome to Real Madrid".

Kovacic is expected to make his debut for Real during Monday's (AEST) league opener at Sporting Gijon.