The 39-year-old was appointed by Crawley Town in May 2017 and led the club to a 14th-place finish in League Two last season.
Kewell replaces Kevin Nolan, who was sacked last week after a winless start to the season left the Magpies bottom of the Football League.
Kewell's assistant at Crawley, Warren Feeney, also moves to Meadow Lane and the club say that "the arrival of a vastly experienced technical director is imminent" after owner and chairman Alan Hardy committed to a restructure of his football department.
"Having now worked in football for a significant period of time, I have had the opportunity to learn from other clubs what good looks like," Hardy told the official Notts website. "I have therefore decided to appoint a technical director, who will set the club's overall footballing philosophy and be on hand to support and mentor the manager as required.
"Harry will, however, be solely responsible for our first-team squad, having the final say on transfers, tactics and team selection. He has enjoyed an excellent start to his managerial career and I am hugely impressed with his knowledge and attention to detail.
"I thoroughly enjoyed our discussions about the role and have been left with no doubt that he has a fierce ambition to succeed and a real enthusiasm to work for Notts County. I'm excited to see how he implements his exciting methods and look forward to him working with our new technical director."
Kewell will not take charge until after Saturday's home game against Forest Green Rovers.