The acquisition makes QNB Group the largest shareholder in the pan-African bank, with 23.5% stake. QNB purchased 12.5% in Ecobank earlier this month.
Established in 1985, Ecobank has presence in 40 countries, with assets of $23.4bn as at the end of June.
QNB said in a statement: "Today’s acquisition was funded through existing resources and QNB will account for Ecobank as an Associate in accordance with International Financial Reporting Standards.
"The QNB Group stated ambition of being a MEA Icon by 2017 is brought closer to realisation through the potential opportunities and commercial benefits resulting from this partnership. This move further consolidates the growth strategy pursued by The QNB Group over recent years."
Ecobank Transnational group CEO Albert Essien said: "Ecobank is the bank with the largest footprint in sub-Saharan Africa.
"This strategic link with QNB, one of the world’s strongest banks, will enhance Ecobank’s reach in North Africa and the Gulf."