David Samson, a mentor to New Jersey Governor Chris Christie, could be sentenced to up to two years in prison.
United Airlines ended the money-losing route from Newark, New Jersey, to Columbia, South Carolina, three days after Samson resigned.
United CEO Jeff Smisek quit after an investigation into the route.
Mr Smisek has not been charged with any criminal wrongdoing.
Samson was the chairman of the Port Authority of New York and New Jersey, which oversees New York City-area airports.
At the time the route operated, United Airlines was lobbying for improvements at Newark Liberty International Airport, which the Port Authority owns.
Samson told prosecutors that he used the "chairman's flight"' 27 times between October 2011 and January 2014.
He owned a vacation home in Aiken, about 60 miles (96km) south west of Columbia.
After Samson pleaded guilty on Thursday, federal prosecutors also charged Jamie Fox, a former lobbyist for United in the scheme.
Governor Christie named Mr Fox as New Jersey's transportation commissioner in 2014. He resigned in October 2015.
A former New Jersey airport official has pleaded guilty to using his position to get a weekly direct flight to his holiday home.