Berisha was born in Stockholm. His family is of Albanian origin. They moved from Kosovo to Sweden before he was born. His younger brother Veton also plays professional football for Viking Stavanger in Norway. He started football at the local club Egersunds IK. On 20 June 2008, when he was 15 years old, he played his first senior match for EIK against Staal Jørpeland IL in the Norwegian Third Division. His good performance attracted the interest of Viking Stavanger, a top club of Norway. He signed with them in March 2009. In July 2012 Berisha went on to Red Bull Salzburg together with his fellow Norwegian Håvard Nielsen. Unlike Nielsen he was soon part of the starting team of Salzburg.