The Swede was confirmed as the new boss after arriving at Meadow Lane on Tuesday morning with compatriot Sven-Goran Eriksson, County's director of football, to finalise his contract as Ian McParland's successor.
Backe has been friends with Eriksson since the 1980's but the two have only worked together in the recent past - when the 57-year-old was Eriksson's assistant at Manchester City and the Mexico national team.
Like Eriksson, he was on the shortlist to become the next coach of Sweden having won four Danish titles in his own right as a manager with FC Copenhagen and Aalborg.
Backe had been due to discuss the manager's job with the Swedish FA on Tuesday, but instead opted for County after deciding what remains of his managerial career should be at club level.
"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," he told Swedish newspaper Aftonbladet.
"Now I look forward to good results at Notts County. I feel hungry and really motivated to do this. We should go up in the first year, no doubt."
He added on Sky Sports News: "I have been in touch with Sven every week since we left Mexico. He has explained the project to me and it's a big challenge.
"It's the first time for Sven and me to start this kind of project with a team in League Two, but that also makes it very exciting. Trying to build a team from the beginning is something new and everything seems to be there for a great journey."
Eriksson is confident that Backe's experience of managing in different countries makes him the right man for the job.
The former England boss also hopes that the appointment will bring some stability to the club following a turbulent season so far at Meadow Lane.
"He will fit in very well. He knows about the project and what we want to do. I've known him a long time and worked with him and I strongly believe he is the right man for the job - absolutely," said Eriksson.
"He knows football and has a huge experience from many countries. He's a very good coach and manager.
"We have been on the front pages and the back pages many times, sometimes for good reasons, other times not for good reasons, so I hope we can concentrate for the rest of the season only on football.
"We need to do that because it's a tough league and we want to be promoted, but it's not easy and we need to concentrate and focus on football. Promotion has always been the target and Hans knows that."
Backe, who has spent much of his managerial career in Scandinavia but has also had spells at Austrian side Salzburg and Greek giants Panathinaikos, succeeds McParland, who was sacked a fortnight ago following just under two years at the helm.
McParland had been seen as living on borrowed time at the club following its takeover by Munto Finance, the Swiss-based Middle East consortium which brought Eriksson to the club.
The Scot's departure came despite a broadly positive start to the season which sees the club currently in fourth place in the table and only six points behind league leaders Bournemouth.
County's owners have ambitions to lift the club to at least the Championship within the next five years but their plans suffered a setback last month when their most high-profile recruit on the playing side, former England international Sol Campbell, quit just five weeks into a five-year deal after playing only one match.
The ex-Tottenham, Arsenal and Portsmouth defender subsequently claimed he had been let down by the club's alleged failure to honour assurances that other top players - such as Roberto Carlos and Benjani - would be signed.
And Backe's appointment has been tempered by the news that Campbell has called in players' union chief Gordon Taylor after allegedly being threatened with a five-year gagging order.
County are refusing to release Campbell's registration so he can sign for another club until an agreement is reached on a 'statement of departure'.
The 35-year-old is refusing to sign the gagging order as he wants to reveal the truth about his short spell at Meadow Lane and has turned to PFA chief executive Taylor to resolve the situation.
"Our view is that a gagging order is an infringement of Sol's - or anyone's - right to freedom of speech," Taylor told BBC Radio 5 Live. "I'm trying to agree a deal so the player can move on and the club can move on.
"We are trying to agree a form of words, a statement that both sides are prepared to accept.
"It's best for both club and player we do this as quickly as possible, because it's an untenable situation."
Campbell has been training with former club Arsenal but Gunners boss Arsene Wenger has confirmed he will not be making a move for his former captain. Championship side West Brom have also been linked with the centre-half.