After 25 years in Minneapolis at a theatre he co-founded, Rothstein will succeed longtime artistic director Michael Donald Edwards at Asolo.
Bethany Brinton, Crystal Manich, and Celeste Moreno are this year’s recipients.
Woster will leave her role at the end of the month, with Jean Hartmann stepping as interim managing director.
The Minneapolis company will present five virtual cabarets in 2021.
In lieu of a 2020-21 season, the musical theatre-focused Minneapolis theatre will reinvest in artists.
The NEXT Generation Commission has been awarded to Kate Kilbane and Dan Moses, and Jessie Austrian and Noah Brody.
The Twin Cities theatre will support the creation and development of new musicals by women and artists of color.
Founded in 1998, the Twin Cities company is focused on exploring and advancing musical theatre.
Woster replaces interim managing director Robin Gillette.
Three new works will be developed this summer at the Minnesota theatre.