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Although the goal of establishing a business school at Rice had been set in the sixties during the admihnistration of University President Kenneth Pitzer, the challenge of raising sufficient funds was not fully met until large gifts like a pledge of $5 million by Houston Endowment, Inc. had been secured in the mid-70's. The intent of this gift was to honor the memory of Jesse H. Jones, one of Houston's most important business and civic leaders and the founder of the Endowment. Thus, the Rice Board named the new school the Jesse H. Jones Graduate School of Administration. In April 1876 Robert R. Sterling, already at Rice as the first Jesse H. Jones Professor of Management and chairman of the accounting department, was named the first dean. In this early period there were two main goals: to develop a coherent curriculum and to build on the Houston Endowment $5 million gift to raise the endowment to levels adequate to support the school's ongoing expenses.

Classes began with 55 students in 1977. Two degrees were offered, the Master of Business and Public Management and the Master of Accounting. In July 1980 Dean Sterling left the Jones, School, having built an excellent faculty, attracted good students, and seen the school begin to achieve a solid reputation in the Houston area.

The primary goal of a second phase, which was to last through the next 15 years and the next two deans, was to realize the ambition for national prominence. Dean Sterling was succeeded by Doug Tuggle, who had been the school's associate dean since 1978 and interim dean in the 1980-81 academic year. He served until 1987, when Rice chose former Postmaster General Benjamin F. Bailar to lead the school. In the intervening period the school moved away from its intense focus on public policy, and in the fall of 1985 the university faculty approved a change in the degree offered by the Jones School from Master of Business Management and Public Management to Master of Business Administration. Additionally, the school opened its own placement office (instead of depending on the university's placement personnel). After a major fundraising effort, the goal of $10 million for a new building and an endowment for its maintenance was reached. Herring Hall, the Jones' School new home, was completed in 1984.

Dean Bailar's administration, lasting until his retirment in 1997, was a period of gradual improvements in program offerings including cooperation with Rice's George R. Brown School of Engineering to offer a joint MBA/Master of Engineering degree. However, the challenges were still not enough to bring the Jones School to the level of being regarding nationally as an elite program.

The arrival of Rice's sixth president, Malcolm Gillis, in 1993, along with Dean Bailar's 1995 paper "Recognition for Excellence," prompted a thorough review of the school. The conclusion of the review was that the Jones School should either "embark on a course of becoming recognized for world-class distinctiveness and quality in management education, or it should decide to close its doors." Determination to follow the first of these alternatives led to commitment by President Gillis and a steering committee to make changes that would take advantage of the school's unique situation in relation to the Houston business community.

The retirement of Dean Bailar was followed by selection of Gilbert R. Whitaker, Jr., a 1953 Rice graduate who as dean of the University of Michigan Business School for nearly 12 years had led that institution to become one of the top business schools in the country. Dean Whitaker announced the goal of being ranked as a top-ten business school within 10 years. He began by leading the school to obtain International Association for Management Education accreditation in 1998. The planning included an increase in the number of studnets and faculty, which, along with changes in technology, made it necessary to anticipate replacing Herring Hall with a new building designed with state of the art facilities for a premier program. Ground was broken on the new building on May 23, 2000, and in August 2002, the school occupied was has become known as McNair Hall.

With these developments, the Jones Graduate School of Business, as it has been known since 2017, has come as close as at any time in its history to being the nationally ranked enterprise envisioned by its leaders since its inception.