Law, who is currently working as the interim coach of Sri Lanka cricket team, is expected to join in July after completing his assignment in England, the Bangladesh Cricket Board (BCB) said at a press conference.
"Law has been appointed as the head coach of Bangladesh cricket team for a two-year period effective from July 1," BCB media committee chief Jalal Yunus said.
"We were in constant touch with Law since May, but he needed a clearance from his present employer Sri Lanka.
"He has got this confirmation recently and already signed an agreement that we sent to him." Law had served as Sri Lanka's assistant coach under Trevor Bayliss since 2009 and was made their interim coach after Bayliss stepped down after the World Cup World Cup 2011.
Law, who played a Test and 54 one-day internationals for Australia, was contracted with Sri Lanka until November this year.
His first assignment with Bangladesh will be overseeing the side for a Test and one-day series in Zimbabwe in August.
"We were looking for a coach who also has the leadership quality," said Yunus. "We found Law as the best option since he has captain Queensland and Lancashire county side before switching to coaching career."
