The deal values the British bank at around 25 million pounds ($40.19 million).
Last year, QIIB had already moved to raise its stake in IBB to 81 percent.
QIIB is offering one pence a share, representing a discount of 70 percent to IBB’s closing share price of 3.38 pence on March 15.
The IBB listed on the London Stock Exchange in October 2004.
“Our long-term strategy is to build an international Shariah-compliant banking business and we believe that our extensive experience in sharia banking will allow us to develop and integrate the IBB business into the QIIB group,” QIIB Chairman Sheikh Khalid bin Thani bin Abdullah Al-Thani said in a statement.
“We look forward to working closely with the existing management of the IBB business and to developing it in the long term,” he added.
Last month, Qatar said it was open to buying stakes in part-nationalized British banks Lloyds and Royal Bank of Scotland.
