"He symbolises what Real Madrid is," said Perez.
Dressed in black suits, white shirts and black ties, the Real Madrid players paraded the trophies at each location, while also signing shirts, giving autographs and posing for photos with their adoring fans.
On top of the bus, the players put on Real Madrid shirts that had the number 14 and 'champions' written on the back.
Karim Benzema and Marcelo shared carrying the Champions League trophy by holding a handle each while Luka Modric and Nacho Fernandez carried the La Liga trophy.
"I haven't slept much, I had too much adrenaline to be able to sleep," said Thibaut Courtois, Real Madrid's goalkeeper who was named man of the match in the final.
"I still couldn't believe it, it's an incredible feeling. For me it's an honour to play for Real Madrid and I hope I can help the team win more."
The Real Madrid bus will arrive at Plaza Cibeles later on Sunday, the central square at the end of Gran Via, where the club traditionally celebrates its biggest titles with supporters around the Cibeles fountain.
After saluting the thousands of fans gathered at Cibeles, the players will ride the bus back to the Santiago Bernabeu for a final celebration ceremony.
