The artistic director will step down at the end of the 2017-18 season.
As Anne and Don Alsedek step down from the company they founded in 1983, they look back on a legacy of education and slow but steady growth.
The arts administrator and performer, previously of Studio Tenn in Nashville, will join the company in August.
After 16 seasons leading the company, Brigden will leave her post as artistic director.
The artistic director of the D.C. theatre will leave the institution he cofounded at the end of the 2017-18 season.
Kraft will leave the company at the end of 2017 after serving 12 years as executive director.
Schlosberg will leave the Alley Theatre to help run another Houston company.
Case comes to the LGBT-focused company after 16 years at La Jolla Playhouse.
Russo has been acting managing director of the company since 2015.
She succeeds Tom Quaintance at the helm of the North Carolina theatre.