Burns, who played 23 Tests and six ODIs for Australia, qualified to play for his adopted country through his mother's side.
Hong Kong overcame a disastrous start to beat Papua New Guinea by 29 runs at the Zayed Cricket Stadium in Abu Dhabi on Thursday and secure a historic berth in the ICC World Twenty20 Bangladesh 2014.
Nepal made history when it qualified for its maiden major ICC event on Wednesday, progressing to the ICC World Twenty20 Bangladesh 2014 by virtue of a five wickets victory over Hong Kong in the ICC World Twenty20 Qualifier UAE 2013 at Zayed Cricket Stadium in Abu Dhabi.