Nelson Broms, (ne Abromowitz) graduated from high school he went on to study business at Baruch College in New York City. He never graduated. Instead, like many young men of his day, he left college in 1940 to enlist in the Army before the country was officially at war. He was assigned to basic training in San Antonio, Texas, at Fort Sam Houston, and later served in Europe as a general staff officer in Third Army Headquarters; ultimately serving on General Patton's staff, he was an assistant G-1 in the quartermaster headquarters of the Ninth United States Army. For his service, Nelson was awarded the Bronze Star in 1945. He retired from the military as a Captain, United States Army Regular having spent seven years on active duty, including the Korean War.

After the war, Nelson's uncle invited him to join his life insurance company where Nelson achieved early success selling group insurance coverage.

In 1956, with an indomitable entrepreneurial spirit, he left to establish the Nelson Broms Company Inc. Always the innovator, Nelson created a new type of life insurance policy to be purchased by apartment building owners in New York. The policies covered tenants, guaranteeing landlords that a deceased tenant's rent would continue to be paid, and, more importantly, allow the tenant's family to remain in their homes and avoid losing their lease.

In 1971, Nelson was recruited by The Equitable Life Assurance Society of the United States (later part of AXA Equitable Life Insurance Company) and served in several senior management roles including chief strategy and marketing officer. He rose quickly in the ranks and was named chairman, chief executive officer, and president of The Equitable Life Holding Corporation. He led efforts to divest the company of international partners and focus on U.S. operations and secure regulatory approval for the conversion from mutual ownership to stock ownership-of The Equitable.

He left The Equitable in 1983 to become a partner of the leveraged buyout management company, Clayton & Dubilier (later Clayton, Dubilier & Rice), one of the oldest, most prestigious private equity investment firms in the world.

He directly supported the work of Arizona State University (ASU) and served as Strategic Senior Adviser to its President, sharing his views on knowledge, entrepreneurship, intellectual fusion, and social consciousness. In 2012, ASU awarded Nelson its prestigious University Medal of Excellence.

He is survived by his wife of 54 years, Pearl Tasch, his two sons, daughter and grandson. He is also survived by three children from his second marriage, their spouses, five grandchildren, and four great-grandchildren.