The appointment of former Bolton, Newcastle and West Ham midfielder, Nolan, comes a day after local businessman Alan Hardy completed his purchase of the club.
Nolan, 34, spent three months as manager of east London side Leyton Orient from January last year, before he was sacked by the club.
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New club owner Hardy said at the time of his appointment a new manager was set to be announced imminently.
Kevin Nolan Newcastle United
Image credit: Reuters
"Kevin is an outstanding leader. We have 20 games left and we need immediate change on the pitch to ensure our EFL safety," Hardy said as he unveiled Nolan.
Nolan added: "I am delighted to be offered the job and I am looking forward to a top day on Saturday.
"It will be difficult but I have never been one to shy away form a fight."
Notts County have lost their last 10games and have been without a manager since January 2 when John Sheridan was sacked.
The club is currently under a transfer embargo because of unpaid bills and have a court hearing with HMRC pending, with Hardy saying he did not know if the embargo would be lifted in time to make use of the January transfer window.
"I cannot say the embargo will be lifted on Monday. My solicitors are now working to resolve that situation," he said.
He added that he expected to appoint an academy director on Friday, who he said would be coming from West Bromwich Albion.
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