University officials said the donation will make it possible to complete the concert hall and adjoining lawn and commons in time to open the center for the 2012-13 season.
"We deeply care about the communities we live and work in," the Weills said in a statement. "When we first toured the Green Music Center, we were immediately inspired by the beauty, the acoustics, and the wonderful potential for this spectacular arts venue."
The complex will be known as the Joan and Sanford I. Weill Hall, Lawn and Commons. The 1,400-seat hall is modeled after Seiji Ozawa Hall at Tanglewood Music Center in the Berkshire Mountains in Massachusetts.
The back wall of the hall will open to a landscaped and terraced lawn that will accommodate 3,000 guests.
The Weill Commons area, directly east of the main concert hall, will be transformed into a 10,000-seat amphitheater for large outdoor events.
"We are passionate about education, music and the arts and we are firm believers that they can help bridge cultural divides that exist in the world," the Weills said.
The initial concept for the Green Music Center began with philanthropists Donald and Maureen Green's dream to establish a choral recital hall on the SSU campus and expand it into a world-class arts center.
The university has received $62 million in donations toward the $120 million music center.
The Greens, who donated $10 million, visited Tanglewood with SSU President Ruben Arminana and his wife Marne Olson in the early 1990s.
They were impressed by Ozawa Hall's acoustical perfection and intrigued by its design, and became determined to replicate it at Sonoma State University.
The Green Music Center also includes a state-of-the-art music education building, faculty offices, a restaurant and executive retreat center.
It also will include the 250-seat "Schroeder's Recital Hall" named by Jean Schulz, wife of the late cartoonist Charles Schulz.
The Santa Rosa Symphony will be the Green Music Center's orchestra-in-residence.
Sanford I. Weill, 78, has been chair of the board of trustees of Carnegie Hall since 1991 and chairman emeritus of Citigroup.
Joan Weill, 76, has served as chair of the board of the Alvin Ailey American Dance Foundation. The Joan Weill School of Dance at Alvin Ailey, completed in 2005, is the nation's largest facility dedicated to dance.
The couple received the 2009 Carnegie Medal of Philanthropy Award and have been married for 55 years.