Whyman succeeds Bristol Old Vic's Emma Stenning, who steps down after four years in the post.
According to a press statement, Whyman will work with artistic director Paul Robinson and executive director Jeremy Woodhouse to "continue to build Theatre503’s strong reputation for staging plays by first time writers".
Robinson said of the appointment: I have been a huge fan of Erica's for over ten years, when she made The Gate pulse with excitement. She's been inspiring to me personally as an artistic director and director and I’m certainly hoping some of that will rub off."
Whyman, who was until recently artistic director of Northern Stage, added: "I am delighted to be joining the Board at this exciting time for Theatre503. I very much admire Paul's ambition for the company and his energetic and talented team, who are looking to the future with great purpose and vigour. I look forward to being able to play a part in ensuring they can realise their vision and secure long-term success."