The 29-year-old travelled to Turin last night and will complete a medical this morning after one source close to the deal described it as "one of the smoothest transfers in years". After years of wrangling, disputes and reconciliation with Arsenal, when Vieira finally did leave, there was little opposition from Wenger and vice-chairman David Dein.
The player is expected to command wages of £85,000-a-week and will also receive an additional fee of £2m payable over his five-year contract. He had just two years remaining on his deal at Arsenal and had already been the subject of interest, once again, from Real Madrid before Juventus moved in to close the deal this week.
Arsenal are confident they can secure the signing of Lyon's Malian international Mahamadou Diarra, 24, this month as a replacement for Vieira.
As he left the club he joined from Milan for £3.5m in 1996 - Wenger's first signing - Vieira said that he had departed without any recriminations towards the club and thanked the supporters for their loyalty.
Vieira said: "When you spend nine years at the club, like I did, it is a difficult decision to leave. But in the end you have to make a choice for your future. It was a very difficult decision, but I am happy with it.
"I made the decision to leave because I felt it was time for me to have a new challenge. But that does not mean I was unhappy or that I was having a problem at Arsenal. It was just that I had the feeling I needed to grow and meet a new challenge and Juventus was the best challenge for me.
"I'd like to thank the Arsenal fans. They have been fabulous. Even recently in the street they were saying 'if you are going, then thanks for the last nine years'. That is really touching and it makes me feel that I gave my best for the club. I can go with my head held high. I left shaking the hand of Arsène Wenger and Mr Dein. That was really important to me."
The deal will mean that Arsenal receive £6.9m immediately with an additional £3.4m next July and another £3.4m 12 months after that. Wenger said that he "shared the sadness" of supporters that their captain had left but assured them that the club would be "strong next season".
"I share the sadness with our supporters that Patrick has left us, but on the other hand I would say to them trust us and support us. We'll be strong next season and we need you behind us.
"Patrick was a great player for us, one of the greatest in the club's history and I feel I had a special relationship with him because I made him come here. I think his impact, not only at Arsenal but in English football overall was just tremendous.
"The sad thing is that he leaves us, but the good thing is that he leaves us on a high. His last kick for the club was symbolic as it won us the FA Cup. Patrick will always be special for Arsenal football club, always in our hearts and our minds."
A delegation from the Italian club came to London on Wednesday to meet with Dein and Wenger and were so confident of success that they were back in Turin by yesterday with the final details sorted out by telephone. The Juventus officials who masterminded the deal had come out to visit the previous Wednesday and returned with an offer that they knew would be acceptable to Arsenal.
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