The switch to the different aircraft comes after the airline refused to accept four A320neos last year over issues with their engines.
"We are going to take all A321s, there will be no more A320s," Baker told reporters at a press event in Doha.
The original order with Airbus was for up to 80 planes.
Last month Baker said Qatar Airways was looking at an order combining both types of planes, but this has now been ruled out.
Qatar is considering using engines produced by CFM International, a venture between GE of the United States and France's Safran.
The engines on the cancelled planes were made by Pratt and Whitney.
Baker was speaking at an awards ceremony which crowned Doha's Hamad International as a "five-star" airport, one of only six in the world.
Baker added that the aim was to expand the airport's capacity from the current 50 million annual passengers to 65 million by 2021, a year before the gas-rich emirate hosts the football World Cup.
The Qatar Airways boss also ruled out job cuts for 40,000 Qatar Airways staff.
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