He finished as top scorer for Danish club AC Horsens while on loan in the 2005-06 season, and made his international bow in October 2006.
He scored his first goal for Albania in the friendly defeat against England B last month at Burnley's Turf Moor grounf.
"Over the weekend I flew to Berlin to meet Besart, his agent and club representatives. We have sorted out a deal subject to us getting Besart's registration," said Clarets boss Steve Cotterill.
"What we will have to do now is go to a work permit panel. We have put our application in and are now just waiting for a date to be finalised.
"Besart has agreed a three-year deal and is very much looking forward to coming to England. There were two other clubs in Germany interested who offered more money but he wanted to come to Burnley and England.
"According to his agent there were also two other English clubs keen on him but we were the first to move."