He won the Pulitzer Prize, the National Book Award and the National Book Circle Critics Award all in the same year.
"I think he is seriously mentally ill, and the fact that he is in the White House is very frightening."
Bret Stephens was vetted for the board while at the Wall Street Journal, but couldn't serve after switching papers.
Art Cullen's Pulitzer-winning work showed how agribusiness infiltrated an Iowa battle over pollution from farms.
Other winners include playwright Lynn Nottage and theater critic Hilton Als.
Trump called The Washington Post's David Fahrenthold a "nasty guy."