Svensson became one of Europe's most successful jazz musicians at the turn of the 21st century before his death, at the age of 44, in a scuba diving accident.

With the release of their albums Good Morning Susie Soho (2000) and Strange Place for Snow (2002), the trio drew the attention of United States audiences.

Their subsequent albums, Seven Days of Falling (2003), Viaticum (2005), and Tuesday Wonderland (2006), were equally well received by critics and resulted in several music industry award nominations as well as making the jazz and pop charts.

In addition to his work with e.s.t., Svensson recorded albums with Nils Landgren, Lina Nyberg and Viktoria Tolstoy.

His diving companions, including an instructor and his then 14-year-old son, eventually found him lying unconscious on the seabed.