Cherng was born in 1948 in Yangzhou, Jiangsu Province, Republic of China on the northern bank of China’s Yangtze River. His father was Ming-Tsai Cherng, a chef.
He and his family then moved to Taiwan after the Kuomintang was defeated in the Chinese Civil War, and in 1963, his family moved to Yokohama, Japan, where his father had taken a job as a chef.
In 1966, at age 18, he immigrated to the United States to study at an American university. He earned a B.S. degree in Mathematics in 1970 from Baker University in Baldwin City, Kansas, and an M.S. degree in Applied Mathematics from the University of Missouri in 1972. At Baker University he had met his future wife, Peggy Tsiang, born in Burma and raised in Hong Kong, who went on to earn a B.S. degree in Mathematics from Oregon State University in 1971 and a Ph.D. in Electrical Engineering from the University of Missouri.
In 1972, he moved to the Los Angeles area to help his cousin run a restaurant called Ting Ho. After a few months, he found a restaurant in Pasadena to take over.
In June 1973, along with his father Ming Tsai Cherng, they took over a restaurant and started a new Chinese restaurant called Panda Inn in Pasadena, California on Foothill Boulevard, using funds from the family and a Small Business Administration loan. It opened on June 8, 1973. The cuisine was Mandarin more than the usually found Cantonese in the area.
In 1983, Andrew Cherng opened the first Panda Express, a fast food restaurant, at the newly opened Glendale Galleria II mall in Glendale, California. He had been prompted to start the spin off by the developer of the mall who had eaten at Panda Inn and invited Cherng to take a place at the food court.
The company had expanded to 100 restaurants by 1993, with the opening of an outlet at the University of California, Los Angeles.
The chain has become one of the biggest Chinese American family owned fast food chains in the United States. Cherng has stated a preference for keeping the company closely held. However, in 2006 he told USA Today if the company could get a valuation close to that of Chipotle Mexican Grill, he might reconsider his stance. However, in an interview with the The Seattle Times newspaper in 2008, he said he would not be interested in making the company public, arguing they did not need the money and citing concerns with the trouble and expense of dealing with shareholders.
In February 2011, the Cherngs donated $2.5 million to support the Collins College of Hospitality Management at California State Polytechnic University, Pomona.
In March 2017, the California Institute of Technology announced that they were changing the name of its medical engineering department to the Andrew and Peggy Cherng Department of Medical Engineering after receiving a $30 million gift from Andrew and Peggy Cherng. In the following month, the University of Missouri announced receiving a $1.5 million gift from the Cherngs which would benefit the its Honors College.
Andrew and his fiancee, Peggy, who was working for aircraft companies in the Los Angeles area, married in 1975. They have three daughters. Two of their daughters, Andrea and Nicole, work for the Panda company in its corporate headquarters. Their daughter Michelle is a primary/secondary school teacher.
In 2015 it was reported that he and his wife had invested $15.2 million in a beachfront property and home in Honolulu.Since 2010, Cherng has been a member of the Committee of 100, an international, non-profit, non-partisan membership organization that brings a Chinese American perspective to issues concerning Asian Americans and U.S.-China relations.
Member of Fremont College's Program Advisory Committee.
In 2008, Cherng was listed in Forbes' Twenty-Five Notable Chinese-Americans.
In 2008, California State Polytechnic University, Pomona conferred Cherng the honorary degree of Doctor of Humane Letters