The centre-back won a deal at Highbury despite putting in wild tackles on Dennis Bergkamp and Thierry Henry, and then a watching Wenger, while on trial.
Wenger’s decision to sign him was vindicated as the Ivorian was part of the ‘Invincibles’ team that won the Premier League in 2004 without losing a game.
He also won the title with Manchester City and nearly made it a treble with Liverpool under Brendan Rodgers and he made it clear he had come to Parkhead to achieve more success.
When reminded of that first day at Arsenal, 14 years ago, Toure laughed and said: “I was young, I was hungry. I had the chance of a trial at Arsenal and for me training with those top players was not easy. I lost my mind there and tackled the manager.”
However, Wenger saw past the mistake and realised he had a top player on his hands, and it was a close relationship with another manager that helped to convince him to move to Celtic.
Toure, who began a media conference by thanking every Liverpool fan and staff member for their support, said: “First thing I will say... Celtic is a great club and if you are linked with a club like that then of course you will be really, really happy as a football player.
“But at the same time, joining Brendan Rodgers was something really special as well. We have been working together at Liverpool, it was a great time there, and now to come in and work with him again was great.
“He’s a top manager. We nearly won the league with him. We had a great, great season and we were really, really unlucky at the end, otherwise we were going to win the league.
“For me, he is one of the best. He has done well everywhere he went. He did a great job at Swansea and did a great job at Liverpool, and I’m sure he will do a great job at Celtic.
“He is joining one of the best clubs in the world and he just wants to keep this team at that level. When you come to a top club, you have to be able to cope with the pressure and deliver results.
“That’s why he is here, that’s why I am here, and we will give everything we have got to make Celtic a better team.”
Toure, 35, has been working with a personal trainer but was left behind as the Celtic squad travelled to Kazakhstan on Monday afternoon ahead of their Champions League qualifier against Astana.
“I’m fit,” he said. “But of course I have just joined the team and I need time to be ready.
“I can’t tell you when but I am ready right now in my mind and I will give everything I have got every day to be able to help my team-mates.
“I just joined the club and there are players who have been working really hard for two months. The manager is the best guy to make the decision. For me, I stick to anything the manager says because every decision he makes is for the good of the team.
“I will be with them in my heart, I will pray for them as well. Definitely we’ll do it.”
Toure could set for another reunion, with Celtic reportedly attempting to buy his former City team-mate Scott Sinclair from Aston Villa.
“I haven’t spoken to him but he’s a really good player,” said Toure, who has signed a one-year contract.
“He’s a top professional. I think he’s going to be a good player for the club because his attitude is very good as well.”
Norwegian midfielder Kristoffer Ajer has also not travelled to Kazakhstan because of a thumb injury.