Eriksson had been out of work since managing the Ivory Coast at this summer's World Cup in South Africa, where they failed to reach the knock-out stages.
Prior to that, the former Manchester City manager had a seven-month spell as Notts County's director of football having managed Mexico's national team from June 2008 to April 2009.
Leicester, who were recently taken over by a Thai consortium, reached the play-off semi-finals last season under Nigel Pearson, who subsequently left to take charge at Hull City.
On the back of taking Swansea to the brink of the Championship play-offs last season, former Portugal international Sousa was then recruited by Mandaric but oversaw a woeful start to the season, with only five points gathered from Leicester's first nine league matches.
A Carling Cup run including away wins over Leeds and Portsmouth provided some relief.
But with many fans questioning Sousa's tactics and team selection, his fate was sealed by a 6-1 league defeat by Pompey, followed by a 4-3 loss at Norwich.
Eriksson becomes Leicester's seventh manager since former Portsmouth owner Mandaric took over in 2007.
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