Rosenberg akatanga basa rake kukirabhu yekumusha kwake Malmö FF uye akazova Allsvenskan top scorer achiri pachikwereti kuHalmstads BK mumwaka wa2004. Kubudirira kwaRosenberg muAllsvenskan kwakakwezva kufarira kubva kunze kwenyika, uye pakupedzisira akapedzisira atambira makirabhu enhabvu muEurope yese, kusanganisira Werder Bremen muGerman Bundesliga, Ajax muEredivisie, Racing de Santander muLa Liga, uye West Bromwich muChirungu Premier League. Mushure mekudzokera kuMalmö FF muna 2014, Rosenberg akarova zvibodzwa zvakati wandei mumutambo wekirabhu yeEFAFA Champions League uye akabatsira timu kuhwina mukombe weligi. Gore rakatevera, Rosenberg zvakare akaita basa rinokosha mukuchengetedza zvikamu zvikwata zveMalmö FF muChampions League. Akanga achibatanidzwawo mukukunda mamwe mazita maviri akateedzana mu2016
uye 2017, pamwe nekupfuura iyo 2018 <unk> 19 uye 2019 <unk> 20 UEFA Europa League mapoka matanho neMalmö. Nguva yake yechipiri paMalmö FF yakabudirira, sezvo akatumidzwa zita rekuti mutambi wenhabvu mukurusa wekirabhu muzana ramakore rechi21.