Macclesfield-born centre half Brisley, 32, joined Wrexham after leaving SkyBet League Two side Port Vale and has also previously played for Macclesfield Town, Peterborough United, Carlisle United and Notts County.
He had previously spent his entire career in the Football League, and he won the EFL Trophy with Peterborough in 2014.
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“I think all the signings will all be key and play their part this season,” said Vermiglio.
“But Brisley is one of the highest profile as this is the lowest level he's played at.
“He has played National League and above all his career, always been a professional and done well. His experience and know-how will be advantageous for us.
“But they will all be key and that's why I have brought them in. I want a competitive squad.
“I need to get the best out of all the players to get the best out of the team.”
He added: “I am still looking to bring in another two or three players and am in talks with a few at the moment. I hope to get a couple done before the weekend.
“We started off with about 10 trialists, all good players who have played the level or a bit above. I will be looking to get a deal done with one or two of those in the next few days.”
Former Chorley boss Vermiglio has only arrived at Buxton this summer and said: “I have been at the level for about eight years in total now and managed at it for four years.
“Buxton are an up and coming club with lots of aspiration and ambition.
“I never thought I would move away from Chorley.
“But once there was that interest there and I had a conversation, it was something I wanted to explore a bit more - to do something different and to be a part of what looks to be an exciting current time and hopefully exciting future for the club.”