Cubela will replace Claudio Cesario who will continue his career at UniCredit Group but outside ZABA, the Croatian lender said in a statement filed with the Zagreb bourse.
Cesario will step down as ZABA's general manager on January 1, 2020, while the date on which Cubela will take over the post will be announced later, the statement said.
ZABA reported last month that its consolidated net profit fell 12.4% on the year to 1.57 billion kuna ($232 million/211 million euro) in the first nine months of 2019.
It is the largest bank in terms of assets in the Adriatic country of some 4.1 million people.
Its shares traded flat at 61 kuna on the Zagreb bourse by 1320 CET on Wednesday.
(1 euro = 7.4446 kuna)