Ince take over from Craig Short who was sacked by the club last week.
“Paul has a wealth of experience as a player and a solid track record as a manager in the Football League, making him the obvious choice for me when we began our search for a new manager,” Notts County chairman Ray Trew told the club’s official website.
“There were a number of high calibre applications for the position and it was encouraging to see just how attractive a proposition managing Notts County remains to some very prestigious names in the world of football management.
“However, when we met Paul it quickly became clear that he was the ideal candidate, he’d done his homework, had some big ideas and was ready to get stuck in straightaway.”