Eriksson, Notts County director of football, appointed his former assistant as the new manager of the English League Two club, it was announced on Tuesday.
Backe previously worked with his fellow Swede when ex-England coach Eriksson was in charge of Manchester City and the Mexico national side.
“Notts County are pleased to announce the appointment of Hans Backe as the club’s new first-team manager,” said a statement on the Midlands club’s official website.
“Hans has signed a three-year contract and starts his duties with immediate effect.”
Backe, like Eriksson, was on the shortlist to become the next coach of Sweden having won four Danish titles in his own right as a manager with Copenhagen and Aalborg.
Earlier this month County sacked manager Ian McParland, who had been in charge for just under two years.
The Scot had been seen as living on borrowed time at the club following its takeover by Munto Finance, the consortium which brought Eriksson to the club.
McParland’s departure came despite a broadly positive start to the season which sees the club currently in fourth place in the fourth tier of English football and only six points behind leaders Bournemouth.
County’s owners have outlined ambitious plans to lift the club to at least the Championship but their plans suffered a setback last month when their most high-profile recruit on the playing side, former England defender Sol Campbell, quit after playing only one match.
Campbell subsequently claimed he had felt let down by the club’s alleged failure to honour assurances that other top players would be signed, and Eriksson was then forced to deny rumours he was on the brink of quitting.