Viso, 41, currently heads the Hirschorn Gallery and Sculpture Garden at the Smithsonian Institution in Washington D.C. She succeeds long-time Walker Director Kathy Halbreich, who steps down Nov. 1.
Viso says she's familiar with the Walker because it has collaborated with the Hirschorn for years.
"It's an institution that I know through my own experience, but also through its incredible reputation," Viso says. "It really is one of the leading contemporary arts centers in the country, nationally and internationally, and really the one thing that appealed to me to me especially was the inter-disciplinary character of the Walker."
The leader of the Walker's search committee says Viso immediately stood out from the 25 or so potential candidates considered for the post.
Viso has spent 12 years at the Hirshhorn, rising quickly from assistant curator to curator of contemporary art and eventually to become the museum's fourth director in September 2005 at the age of 38. She will remain in the post until Dec. 31.
"In the past 12 years, first as a curator and then as director, I have seen the museum evolve into a vibrant hub for contemporary art, artists and ideas," Viso says.
Viso is credited with shifting the Hirshhorn's focus to more contemporary programs of international art, including more experimental work with timely exhibitions.
Acting Smithsonian Secretary Cristian Samper said Viso helped expand the museum's presence in the art world.
Before coming to the Smithsonian, Viso held positions at the Norton Museum of Art in West Palm Beach, Fla., and the High Museum of Art in Atlanta.
A nationwide search for a new director will begin immediately.
(The Associated Press contributed to this report)