The Whites had originally been set to meet SK Lyn Oslo on the same evening but the friendly was cancelled after the Norwegian club went into bankruptcy.
Brann are regarded as one of the biggest clubs in Norway and have won the Norwegian Premier League on three occasions, the most recent being 2007.
But they are currently 12th at the halfway stage of the 2010 season and are just 4 points above the relegation zone.
Former Leeds players Eirik Bakke and Gylfi Einarsson are in the current side.