Braman was born in 1932 in West Chester, Pennsylvania, and grew up in the Cobbs Creek section of Philadelphia, where his Father owned a barbershop. Braman's parents were both Jews who emigrated from Europe. His Romanian-born mother was a seamstress and his Polish Father a barber. Braman was a water boy in his teenage years at the Eagles training camp, which was then in West Chester. During the season, he would sneak into Shibe Park to watch the team play. Braman attended West Philadelphia High School and graduated from Temple University in 1955 with a degree in Business administration.
He began his career in 1955 in the marketing and sales department for Seagram's Distributors. In 1957, he founded Keystone Stores, a chain of self-service department stores, in Philadelphia. In 1964, he organized Philadelphia Pharmaceuticals and Cosmetics, a manufacturer of pharmaceuticals and was President and Chief Executive Officer.
In 1972, he bought a Cadillac dealership in Tampa. Three years later he bought another in Miami and today he is CEO of Braman Enterprises, an umbrella company for his Automotive businesses that include more than 20 car dealerships in Florida and Colorado selling Acura, Audi, Bentley, BMW, Bugatti, Cadillac, Genesis, Honda, Hyundai, Kia, Mercedes-Benz, MINI, Porsche and Rolls-Royce.
In 1982, he led a successful campaign against a city sales tax that would have renovated the Miami Orange Bowl for Dolphins owner Joe Robbie. From 1985 to 1994, he owned the Philadelphia Eagles football team, having purchased it from Leonard Tose. During Braman's time as owner, the Eagles were NFL NFC Eastern Division champion in 1988 and won at least 10 games for five straight years through 1993.
Braman served on the Board of Governors of various institutions. In 1999, he helped defeat then-County Mayor Alex Penelas campaign for a one-cent sales tax that could have generated billions of dollars to spend on mass transit, while potentially hurting automobile sales.
He financially supported a recall election against Miami-Dade Mayor Carlos Alvarez because of a huge property tax increase and pay hikes to Alvarez's top staffers. On March 15, 2011 close to 90% of those that turned out to vote that day in Miami-Dade County, voted to recall the mayor. It is believed to be one of the most lopsided recall elections in the history of American elections.
Braman is a supporter of Marco Rubio, and was considering spending anywhere between US$10 million to US$25 million in support of his 2016 presidential campaign. According to the acknowledgements in his autobiography, Rubio has thanked Braman for being a supporter, and Braman has employed at one time or another Marco Rubio's wife, Jeanette Dousdebes Rubio, at Braman Family Charitable Foundation.