Mjallby -- better known as Big Dolph by fans -- was signed by Dr Jo Venglos from Swedish club AIK in 1998.
He had four great seasons as a stalwart in Celtic's defence but his career was hit hard by a series of injuries and operations during the last two seasons before his contract expired in May.
The 33-year-old has signed a two-year deal with Levante, who have just been promoted to Spain's top league.
It is believed Celtic offered Mjallby a one-year deal but his decision not to take it up came as little surprise as he had struggle to regain fitness and form last season.
The Spanish move was a surprise to his old club, AIK, however as they believed he would return home to rejoin them after Euro2004.
Perhaps the thought of lining up against old club-mate Henrik Larsson -- now at Barcelona -- was too tempting for the Swedish defender.
Mjallby has played for his country 45 times and led out the team as captain for the pre-tournament friendly with England. But he stayed on the bench throughout Sweden's period in the tournament.
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