Russo has been acting managing director of the company since 2015.
She succeeds Tom Quaintance at the helm of the North Carolina theatre.
The performer/composer/music director will be artistic director of the center’s lab for musical theatre development.
Bradshaw will step into the leadership role after serving as the company’s interim managing director since last July.
Ivers will succeed David Ira Goldstein in the role this July.
Byrd, formerly of Tennessee’s Clarence Brown Theatre, will begin his new role in Virginia this July.
He will depart in 2020, after 50 years at the theatre he founded.
The former principal dancer at the New York City Ballet will assume the new role in July 2018.
Melillo’s departure is part of a series of planned leadership transitions.
Steward will move from Dallas to Boston for the new leadership role.