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Bagge was in the early 1990s member of the group Legacy of Sound. His big break came with him writing the huge hit of 1998, "Because of You" by 98 Degrees, which went platinum in the United States. Bagge specifically desired to work with Janet Jackson, stating "She's the one I would give anything to work with. The ultimate female artist," adding, "let's just say we will definitely be prepared if and when that happens."

He has written and produced songs for Janet Jackson, Celine Dion, Madonna, Santana, Jennifer Lopez, Nick Lachey, Jessica Simpson, Samantha Mumba, Lara Fabian, Enrique Iglesias, Ace of Base and Ashley Tisdale.

Bagge was awarded Best Pop Song at the BMI London Awards for producing Janet Jackson's "All Nite (Don't Stop)." Bagge with Laila Bagge Wahlgren and Andreas Carlsson was jury in Idol 2008, Idol 2009 and Idol 2010 in Sweden. In 2009 and 2010 he was with the program Made in Sweden, where Bagge, Carlsson and Laila Wahlgren would search to find recording artists. IN 2009, the program featured Kim Fransson and Janet Leon. In 2010, it was for recording a single by the Swedish girl pop group Play.

Anders Bagge has also produced Safura Alizadeh in her song "Drip Drop" representing Azerbaijan's entry in the Eurovision Song Contest 2010.

Bagge co-wrote Azerbaijan's entry in the Eurovision Song Contest 2012, "When the Music Dies", performed by Sabina Babayeva.