Adam Bock, Bruce Coughlin, and Mimi Lien have also been selected.
The annual Village Voice theater awards helped launch the careers of artists such as Meryl Streep, Al Pacino, Samuel Beckett.
The Wing will now copresent the awards with The Village Voice.
How I Met Your Mother's Cristin Milioti will be among the evening's presenters.
Feingold ended his decades-long tenure as the publication's chief theater critic in May 2013.