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The former England international revealed that after meeting Chester's chairman, his mind was made up.
"I've been impressed by the club's chairman, Stephen Vaughan, and he has the same sort of aspirations for the club that I do," said Wright.
"On a personal level it's pleasing to be back in football so quickly. Obviously our first objective is to avoid relegation, and then we can look forward to next season and a bright future."
Wright resigned as manager of Oxford United in November last year following allegations that he made racist remarks at a black match official. He has signed a three year contract at the Deva Stadium.