Wright, 45, who took City back into the Football League in 2004 after a four-year stay in the Conference, started his third spell in charge of the club in November.
Things initially went well as Wright clocked up three wins in little over a month. But he was working without a contract as the financially struggling, badly-supported club struggled under the weight of a reported £7m debt. And his latest departure has come as little surprise to disillusioned City fans.
"I've won this league," said Wright. "Do I want to be there again? I'd rather not!"
Wright was briefly linked to the vacant Tranmere manager's role before it was filled by fellow former Liverpool player John Barnes.
Last week Vaughan denied that he was trying to lure former City assistant manager Malcolm Thompson, who left for Inverness Caledonian Thistle in December 2007, back to the Deva Stadium.
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