The club's communications director Sophie McGill confirmed that the former Barnsley coach had been offered the post on a permanent basis immediately following the victory over Droylsden.
A delighted Walker duly accepted and replaces Billy McEwan, who was dismissed by the club last month after two-and-a-half years in charge.
Walker commented : "I'm very proud to accept this position but there's a lot of hard work ahead.
"I want to get this club back into the league and then who knows what might happen."
The Minstermen have remained unbeaten under Walker's temporary leadership, winning five times and drawing once.
Source: www.minstermen.net