The 46-year-old filmmaker has heaped praise on the action movie icon and martial arts star, and recalled the moment he first saw him in 'Rumble In The Bronx'.
Speaking to SFX magazine, he said: ''The first time I saw a Jackie Chan film at the cinema was 'Rumble In The Bronx', at the Princes Charles in London. It was absolutely rammed.
''It felt like everybody was watching a Jackie Chan film on the big screen for the first time. I cried at the end when Jackie turned to the camera and did a thumbs-up.
''I remember being so happy that something that had felt like, in the Western world, a cult phenomenon for so long, had broken through. That's an amazing thing.''
Wright - who was a child when he first saw Chan in 'The Cannonball Run' when it aired on television - heaped praise on the star's skills and the ''connection'' he had with his audiences.
He added: ''The thing about Jackie Chan is this everyman quality. He has a connection with the audience.
''The fights are incredible. There's this whole other level where there's some insane stunt where you can't believe somebody is doing on camera.''
The 'Shaun of the Dead' director also admires the way Chan will what needs to be done to create a perfect shot.
Wright explained: ''Jackie is willing to let himself get really beaten up on screen. That's always a key element of the films.
''Seeing Jackie Chan take a punch is as important and dramatic as him winning.''
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