The 29-year-old was "proud" of his ï¿½13.7million move to Italian champions Juventus, despite suggestions the Gunners gave him little choice once a fee was agreed.
While Arsene Wenger's side were a dominant in domestic competition with Vieira as captain, they did not achieve the same success in Europe's premier club competition.
Vieira said: "When you spend nine years somewhere it is difficult (to leave). When you make a decision you must think about what you want to achieve."
"You never know what will happen in the future, but when you think about it we won almost everything with Arsenal. The only trophy missing is the Champions League.
"And when you think that the year before last Porto won it, then you think anyone can win it. I think we have been really unlucky in that competition.
"But when I look back overall on my nine years it has been fantastic. It doesn't matter what some people say, I hope they remember I played more than 400 games for the club."
Vieira, whose final kick for Arsenal clinched the FA Cup in a penalty shoot-out against Manchester United at Cardiff's Millennium Stadium in May, insists he still has nothing to prove in Italy despite an undistinguished spell there 10 years ago with AC Milan.
He added today: "I have nothing to prove to anybody. I think I have proved how good I am in the last nine years at Arsenal. When I went to Milan (from Cannes) I was 19. Now I am 29. It is not the same.
"I am going now after winning many trophies and I have a different stature after nine years at Arsenal. Every aspect of my game has improved a lot. I have a strong belief in myself."
Vieira twice helped Arsenal win Premiership and FA Cup doubles in 1998 and 2002 and said the club would always be in his heart, adding: "The fans were always fantastic to me and when I went to the training ground to say goodbye to everyone it was quite emotional.
"The medical staff, the office people, the kitchen staff, the chef, I know them all well and my relationship with them has been fantastic.
"It is just a special club. They create a very special atmosphere for the players to work in. That is very important. I am sure that will be really difficult to find again."
Vieira will now rejoin Fabio Capello, his coach when the fledgling France star played at Milan in 1996, but he believes Wenger to be his mentor.
He said: "He is the one who really knows me. He has been fantastic to me.
"When I had bad moments he gave me 100% support and confidence. That was important. I'd also like to say thank you to Mr David Dein (vice chairman) who believed in me and trusted me."
"I remember the boss (Capello) well. I was only young and there was never much room in the team for me but he always found the right words to keep me motivated.
"I have come to Italy now as a big-name winner of several trophies with Arsenal and intend to stay on that path with Juve. It is a great challenge and a fantastic achievement to be here, but I am ready for it."
Juventus director Luciano Moggi, who master-minded the capture of Vieira, claimed he had to fight off interest from Real Madrid - who Vieira was linked with last summer.
Moggi said: "No wonder it was difficult to strike a deal when Real Madrid did all they could to sign him and Arsenal did all they could to keep him, but Patrick chose Juve and now an important player is on board, one of the best midfielders in Europe."