The 43-year-old was unveiled as the club's fourth manager since reformation, following Jon McCarthy, who was sacked two weeks ago.
Chester have had a torrid start to the Vanarama National League season, sitting in the relegation zone with eight points from 11 games.
They've gone 14 home matches without a win and now new boss Bignot promises to get results.
"I can't wait to get started and meet the players at training tomorrow," he said.
"I felt my next job was important where I had an opportunity to bring success and for me Chester provides that.
"I'm definitely confident we can turn things around, and we will. I'm sure the supporters will see a group who are organised and have a structure to their play both on and off the ball. They'll have clear roles and responsibilities and I honestly believe that they'll draw confidence from that.
"I've done a lot of background into the squad, I've pretty much gone through all the season's games. I have a clear understanding of where the group's at and Tom Shaw will be pivotal in that as well.
"The remit for me, right here right now, is to get results and start climbing up the table. In time we will evolve into where we want to get to."
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