Yeung, the 53-year-old Hong Kong businessman who has owned the Championship (second tier) club since 2009, is awaiting the verdict, due later this month, of a money laundering trial in Hong Kong, an offence he denies.
"Mr Yeung, with his foresight, aspiration and clairvoyance, has steered the board successfully through landmark projects such as the acquisition of Birmingham City Football Club, for which the board is profoundly indebted," BIHL said in its statement.
"Mr Yeung unequivocally confirms that he has no disagreement with the board and that there are no other matters relating to his resignation that are required to be brought to the attention of the shareholders of the company."
Birmingham are 18th in the Championship, six points clear of the relegation zone, and face fellow strugglers Charlton Athletic on Saturday.
They won the English League Cup in 2011 - beating Arsenal at Wembley - but were relegated from the Premier League in the same season.
(Reporting by Michael Hann, editing by Stephen Wood)
