Housing secretary Michael Gove has also decided to take over the plans, rather than letting Leeds City Council make the decision.
The secretary will normally only do this if the application conflicts with national policy in "important ways", or is nationally significant.
With large investment in the scheme so far, airport bosses said they were "not prepared to commit a further uncapped sum over an indefinite time frame" into a public inquiry process when their focus "needs to be" on modernising the airport for the future.
The airport will now turn its attention to developing an extension to the existing terminal, originally approved by Leeds council in 2019.
