He will stay on till the end of June, when his contract expires.
His decision to quit comes less than a month after Bangladesh reached the final of the Asia Cup, widely seen as one of their finest achievements.
“It is with great regret and a heavy heart that today I announce my stepping down as the head coach of Bangladesh,” Law said.
He said he will move back to Australia, after two and a half years in subcontinent, which included a coaching stint with Sri Lanka. “It is personal reason as to why I am standing down. Living away from the family and not seeing people growing up, I think we all understand that family comes first,” he said. “Cricket has been a huge part of my life but over the years I have realised that there is nothing more important than the family and if they are not happy then I am not happy and something had to give.”
Law had taken over as national coach last July, and though the initial results were disappointing – including losses to Zimbabwe – the home season ended with Bangladesh upsetting India and Sri Lanka in the Asia Cup, before losing the final in a last-ball finish.
Bangladesh media committee chairman Jalal Yunus said the board understood Law’s decision. “As he (Law) has said the family was his priority and that should be the case for all of us,” Yunus said. “We are sorry to see him go, especially at a time when under his guidance the Bangladesh team is doing really well and showing good consistency.”