Backe arrived at the club accompanied by countryman Sven-Goran Eriksson, director of football at County, on Tuesday morning.
County have entrusted Eriksson with the task of finding a new manager, and it seems he has turned to his former assistant at both Manchester City and the Mexico national team.
Like Eriksson, Backe was on the shortlist to become the next head coach of the Sweden national team, but he insists he is keen to get back into club management.
"It's 99% a done deal for me to join Notts County," he told the Nottingham Evening Post.
"I want to get back into the daily routine with practice, I've felt a longing for a long time now. It's possible that the next two to three years will be my last as a club manager."
Backe has spent much of his managerial career in Scandinavia and has won four Danish titles with FC Copenhagen and Aalborg.
He has also had spells at Austrian side SV Salzburg and Greek giants Panathinaikos.
Notts County's last two matches have been overseen by joint caretaker team Dave Kevan and Michael Johnson, but it seems likely that Backe will be in charge for for the home game against Shrewsbury at the weekend.