The announcement was expected to be made at a conference in the southern Polish city of Katowice.
Bańka was in May picked to be the new head of the international drug-fighting body beginning next year.
He was at the time selected over Marcos Diaz of the Dominican Republic at a meeting of government representatives in Montreal, Canada.
The Pole, 35, is set to take over as the organisation’s new head effective January 1.
The former 400-metres runner-turned-politician was in 2017 appointed a member of the executive committee of the international sports doping watchdog.
In January he won a key vote by a committee within the Council of Europe to become Europe’s candidate to succeed outgoing WADA President Craig Reedie.
The World Anti-Doping Agency was established in 1999 as an international, independent organisation funded by sports bodies and governments.
In 2017, a new Polish Anti-Doping Agency (POLADA) began operating to step up the fight against drug cheats in sports.
Bańka on Tuesday vowed to make every effort to keep sports “clean” from doping cheats.