"I adore Arsene Wenger, for his intellect, his language skill (knowing seven different languages is a feat!) and many more reasons", said the 29-year-old.
Speaking on RTÉ Radio's News at One, Hamilton said: "I think what has changed is what has happened on the pitch".
Attention has already turned to candidates to take over the role, with Celtic boss Brendan Rodgers, Thomas Tuchel, Carlo Ancelotti and Luis Enrique among the favourites.
And Arsenal's famous supporters have shared their reactions to his departure.
The Gunners are a distant sixth in the league, 14 points adrift of fourth-placed North London rivals Tottenham Hotspur with five games remaining. The team, however, has failed in the playoffs both years, getting the boot in the conference semifinals. The team allowed just 26 goals in those matches, with the defensive pairing of Sol Campbell and Kolo Toure dominating week in and week out. He is a proper football man, he lives and breathes it, he's dedicated to his job and his sport.
The Frenchman has lifted the FA Cup in three of the last four seasons but that has not been enough to appease some supporters.
"I hope my son can be intellectual like Arsene Wenger, and brave like (Arsenal midfielder) Jack Wilshere", he added.
For trusting me as a teenager, giving me the opportunity to express myself and grow both as a footballer and as a person. "The Premier League is about huge personalities like Arsene", said Guardiola. "The club has been relying on German know-how for several years now". Put simply, that is an entertaining style of football, opportunities for young players and a fiscal structure that safeguards the club's long-term future.
"It is power against power, it is quality against quality, it is ambition against ambition".
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It led to the left back making a dramatic move across London to Stamford Bridge in 2006, amid allegations of tapping up. I think your question is a typical question from somebody who was not on this side: not a manager, not a player.
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As I took to my bed last night feeling drained and exhausted I was searching for why I had been feeling so emotional all day. This article has been produced by Scroll Brand Studio on behalf of TVS Racing and not by the Scroll editorial team .
Meet the man who named his son after Arsene Wenger
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