In the early 1970s, Simpson moved to Los Angeles and got a job marketing exploitation films for Warner Bros. In 1973, Simpson got a job at Paramount Pictures. While there, he co-wrote the 1976 film Cannonball, in which he also had a small role. By 1981, he was named President of production at Paramount.

As Simpson and Bruckheimer's success grew, so did Simpson's reputation for being a brash "party animal". He had been using cocaine since the 1980s, but increased his usage over the years. His excessive spending (in both films and his personal life) and erratic mood swings caused by his drug use were well known within the Hollywood industry by the 1990s. According to Screenwriter James Toback, both David Geffen and Jeffrey Katzenberg had attempted to get Simpson to go to rehab for his drug use.

Simpson left Paramount in 1982 and forged a partnership with fellow Producer Jerry Bruckheimer. The two would go on to produce some of the most financially successful films of the 1980s: Flashdance (1983), Beverly Hills Cop (1984), Top Gun (1986) and Beverly Hills Cop II (1987). In 1985 and again in 1988, he and Bruckheimer were named Producers of the Year by the National Association of Theatre Owners.

In 1990, Simpson and Bruckheimer signed a five-year deal with Paramount worth a reported $300 million. The deal would prove to be short lived. Later that year, the Simpson/Bruckheimer-produced Days of Thunder starring Tom Cruise was released. The auto racing film received mixed reviews and grossed $158 million (over a $60 million budget). While the film was still a financial success, it did not match the success of Simpson and Bruckheimer's previous films. Simpson and Bruckheimer blamed Paramount for the film's lackluster box office returns stating that the studio rushed the planning and release of the film. In turn, Paramount blamed the film's performance on Simpson and Bruckheimer's overspending. The duo mutually parted with Paramount shortly thereafter.

In 1991, the two signed with Disney. Their first film for Disney, The Ref (1994), was a financial flop. Their following films, Dangerous Minds, Crimson Tide, and Bad Boys, all released in 1995, brought the pair back to success.

Frustrated with Simpson's escalating drug use and declining work, Jerry Bruckheimer terminated their partnership in December 1995. The two agreed to finish work on The Rock, which was already in production. The Rock was released after Simpson's death and is dedicated to his memory.

On January 19, 1996, Simpson was found dead in the bathroom of his Bel Air, Los Angeles home. His death was initially attributed to "natural causes". An autopsy and toxicology report later determined that Simpson had died of heart failure caused by combined drug intoxication (cocaine and prescription medications). At the time of his death, there were twenty-one different drugs in his system including antidepressants, stimulants, sedatives, and tranquilizers. In August 1996, investigative reporter Chuck Philips of The Los Angeles Times revealed that Simpson had been obtaining large quantities of prescription drugs from fifteen different doctors and that police found 2,200 prescription pills in his home.

A 1998 book by Journalist Charles Fleming reported that Simpson's prescription drug expenses were over $60,000 a month at the time of his death.