Allback joined Aston Villa for a cut-price fee of £2million in May 2002 from Dutch club Heerenveen. The striker had a clause in his contract that allowed him to move for that amount between May 15 and the end of the month.
The former Lyngby, Bari and Orgryte IS player was actually valued at around £4million.
Allback broke off from Sweden's preparations for the World Cup Finals to jet into Birmingham and sign a three-year contract with an option for a fourth.
The 28-year-old had also been pursued by Sunderland, Rangers, Feyenoord and PSV Eindhoven. But he said: 'Moving to Villa felt right and this is a great time for me.
'I listened to Olof (Villa defender Mellberg) and he told me that Villa was the right club for me. Villa are a big club with fine traditions and Olof has only had good things to say about them.'
Manager Graham Taylor added: 'I had been watching him for a long time and my coach at Villa, Stuart Gray, tried to sign him when he was in charge at Southampton. When I found out about the clause he had in his contract I acted as soon as I could.'
Scored four times in his six World Cup qualifying appearances and is said to be the perfect foil for the predatory Larsson.
Played in all four of Sweden's games at the finals, including the 1-1 draw with England in Saitama, as they reached the second round.
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