After her studies at University College of Opera in Stockholm, she made her debut as Susanna in 1998. She has been a member of the Swedish National Opera, where she has sung Susanna, Pamina (The Magic Flute), Tebaldo (Don Carlos), Gretel (Hansel und Gretel), and Sophie. In 2010 King Carl XVI Gustav of Sweden appointed her a court singer.

Persson has sung at a number of the world's leading opera houses and festivals, including Paris Opéra, Théâtre de la Monnaie, Aix-en-Provence Festival, Royal Opera House Covent Garden, Frankfurt Oper, Wiener Staatsoper, Netherlands Opera, and San Francisco Opera. Since 2006 she has been a regular at the Glyndebourne Festival Opera where she has sung Fiordiligi (Così fan tutte), Anne Trulove (The Rake's Progress), Donna Elvira (Don Giovanni), and the Governess (The Turn of the Screw). In 2009, Persson made her debut at the Metropolitan Opera as Sophie and has also sung Fiordiligi and Gretel there.

Persson's recordings include The Creation, The Seasons, Bach cantatas, Mahler's Second and Fourth symphonies, several solo recitals, and DVDs of the Mozart da Ponte operas, L'incoronazione di Poppea, Der Rosenkavalier, and The Rake's Progress.