Jacobs was born in 1940, the son of Genevieve (née Bibby) and Louis Jacobs, the son of Jewish immigrants from Poland. In 1915, his Father and his two brothers, Charles and Marvin, founded a company that first sold concessions in theaters and then expanded to major league ballparks. His Father took over the company in the 1950s when the health of his brothers faltered and Jeremy took over at age 28 when his Father died in 1968.

Jacobs has owned the National Hockey League's Boston Bruins since 1975. Jacobs represents the club on the NHL's Board of Governors and serves on its Executive Committee. At the NHL Board of Governors meeting in June 2007, Jacobs was elected chairman. He replaced the Calgary Flames' Harley Hotchkiss, who stepped down after 12 years.

Jacobs was listed for several years in a row as one of Sports Business Journal's Most Influential People in Sports. He was inducted into the Sports Hall of Fame in Western New York in October 2006.

In 2007, Jacobs donated $1 million to support an endowed chair in immunology at Roswell Park Cancer Institute (RPCI). The gift was made to RPCI's Leaders for Life endowment campaign in honor of Jacobs' brother, the late Dr. Lawrence D. Jacobs, an immunology researcher who died in 2001.

The University at Buffalo received a $10 million gift from Jacobs, his wife Margaret, and other family members on June 11, 2008 to establish the Jacobs Institute. The Jacobs Institute supports research and clinical collaboration on the causes, treatment, and prevention of heart and vascular diseases. This gift was also made in honor of his late brother, Lawrence. The Jacobs' gift was at the time the largest single gift ever made to the University at Buffalo. The donation also made the Jacobs family the university's most generous donor, with gifts totaling $18.4 million. Jacobs has also served the University at Buffalo as chairman, trustee, and Director of its foundation, chairman of the President's Board of Visitors, advisor to the School of Management, and as chairman of the University at Buffalo Council.

In November 2012, Jacobs and his family announced a $1 million donation to the Say Yes Buffalo Scholarship. Say Yes Buffalo is "an education-based initiative that provides a powerful engine for long-term economic development, which will radically improve the life course of public school students in the City of Buffalo."

Jacobs holds honorary doctorates from the University at Buffalo, Canisius College, Johnson and Wales University, and Niagara University, where he was awarded an honorary Doctor of commercial science in October 2013.

in 2015, Jacobs received the Lester Patrick Award. This award honors outstanding Service to hockey in the United States. The award committee stated, "Jeremy Jacobs — as owner for 41 years of the NHL's first US-based team and long-serving Chairman of our Board of Governors — has provided unparalleled vision, innovation and inspiration to the advancement of hockey and the NHL." Jacobs received this award at a ceremony held at the US Hockey Hall of Fame on December 17 in Boston.He was inducted into the Hockey Hall of Fame in 2017 as a builder.