The Gunners will embark on a new era this summer as they recruit a replacement for the Frenchman, who has been at the helm for close to 22 years.
As well as bringing in a new manager, however, Wright believes that further changes are required across the board following a period of stagnation.
"It's sad news for Arsenal Football Club, but I think the time is right," he told the Totally Football Podcast. "If he left after 2014, I think that would have been even better. He wouldn't have had to take all the vitriol he's dealt with. But I think it's right for him and right for the club now.
"This is just the start and I'm not sure if the people upstairs are the right people in charge now. [The club] is not in great shape, from a management level, recruitment level and players' attitudes. And then obviously how the fans feel at the moment.
"There's a lot of hard work to be done in terms of galvanising the whole place. The next manager that comes in has probably got one of the hardest jobs in football, because Wenger was magnificent.
"I don't think his legacy will be harmed, because he has done such great things. His legacy is fine. He's done magnificent things. But for Arsenal now, not just for Wenger, there are a lot of changes that have to happen: the players, the management and the owner."