Green had recently contracted pneumonia and died in La Jolla, Calif.
"Cecil's leadership helped shape the very foundation of Texas Instruments--respect for people, ethics in business, and the strong belief that we need to give back to our community," said Tom Engibous, chairman, president and CEO of Texas Instruments.
In December 1941, Green joined Eugene McDermott, J. Erik Jonsson and H. Bates Peacock to buy Dallas-based Geophysical Service Inc., the predecessor to Texas Instruments.
During World War II, GSI branched into the production of submarine detection devices for the U.S. military.
In 1951, the company's name was changed to Texas Instruments, and GSI became a subsidiary. Officials introduced electronics production into the business mix.
Texas Instruments had more than $8 billion in revenue last year.
Green, who was born in England, was made an Honorary Knight of the British Empire in 1991 by Queen Elizabeth II.
Green's wife, Ida Mabelle Flansburgh Green, died in 1986. They had no children.