The awards are presented by the Actors' Equity Foundation to honor "the most promising female and male performers on the New York metropolitan scene."
Each will receive $2,000 and an engraved crystal trophy at a ceremony that will be held June 9 in Manhattan at Equity's Eastern Regional Board meeting.
Tveit was recognized for his performance in the Tony-nominated Next to Normal and Bernstine for her work in the Pulitzer Prize-winning Ruined.
Established in 1944 by actor and former Actors' Equity Association President Clarence Derwent, The Derwent Awards are among the oldest awards on Broadway. Past recipients include Annette Bening, Kristin Chenoweth, Calista Flockhart, Gene Hackman, Dana Ivey, John Malkovich, Ann Reinking, George C. Scott, Frances Sternhagen, Gene Wilder and James Woods. Zoe Kazan and Michael Esper were last year's winners.
Bernstine has also been seen onstage in The Misanthrope, Chicken, A Small Melodramatic Story, 'nami, (I am) Nobody's Lunch, The Ladies, Paris Commune and Matt & Ben. Her screen credits include "Chappelle's Show," "Law & Order" and "Rachel Getting Married."
The Judges' Panel included Joe Dziemianowicz, Daily News; Adam Feldman, Time Out NY; Susan Haskins, Theatre Talk; Michael Kuchwara, Associated Press; and David Rosenberg, Back Stage.