Raised in a Jewish family in Danville, Illinois, Azoff began promoting and booking bands while a student at Danville High School and then in college at the University of Illinois at Urbana–Champaign. His first management client was Champaign-based REO Speedwagon; his second was Dan Fogelberg. In 1972, Azoff headed to Los Angeles with Fogelberg. He worked for Geffen-Roberts Management and there began working with the Eagles, a relationship that has lasted more than forty years. During his career he has worked as an agent, personal manager, concert promoter, movie producer, independent record label owner, merchandiser, music publisher, and CEO of a record company.

From 1983 to 1989, Azoff was chairman of MCA Music Entertainment Group and is credited for turning around that label’s fortunes.

In October 2008, ticketing and marketing company Ticketmaster announced they would acquire the management company Front Line Management Group, Inc. As part of the deal, Azoff, who was founder and chief executive officer of Front Line, became chief executive officer of Ticketmaster and was named chairman of Live Nation in February 2011.

The merger faced many legal hurdles and opposition. The merger was opposed by members of the United States Congress, business rivals such as AEG Live, the Computer & Communications Industry Association (CCIA), whose members include Google, Oracle, Microsoft, Yahoo, Intuit, and eBay. Despite the opposition, the merger was still approved in 2010.

Azoff co-produced the movies Fast Times at Ridgemont High, Urban Cowboy, Jack Frost, Above The Rim, and The Inkwell, and was executive producer of The Hurricane. He has been named “Manager of the Year” by two touring industry trade publications. In 2012, Azoff appeared in Artifact, a documentary film about the modern music business focused on the legal battle between Thirty Seconds to Mars and record label EMI.

In 2012, he topped Billboard Magazine’s Power 100, being named the most powerful person in the music industry. Azoff serves on the boards of iHeartCommunications, Inc. and Starz LLC.

In 2013, Azoff founded the performance rights organisation Global Music Rights. The company administers publishing for artists including Metallica, Bruce Springsteen, John Lennon and George Harrison, Pearl Jam, and Bruno Mars.

In September 2013, Azoff unveiled Azoff MSG Entertainment, a venture with The Madison Square Garden Company (MSG). In addition to his role as chairman and CEO of Azoff MSG Entertainment, Azoff would serve as a consultant to MSG in connection with the management of its live event venues, including the Forum in Inglewood, CA and other MSG-managed buildings.

In 2015, Azoff played a thinly veiled version of himself in the Documentary Now! parody of History of the Eagles.

In 2015, Azoff co-founded Oak View Group along with Tim Leiweke. The company is building the Belmont Park Arena as well as a new arena in Milan, Italy.

In 2018, the United States Department of Justice launched an investigation following complains that Live Nation had engaged in anti-competitive practices following the merger. AEG has alleged that Live Nation had pressured them into using Ticketmaster as a venue. If AEG had refused, they would have lost out on business. The allegations of antitrust violations have resulted in a re-examination of the merger between Ticketmaster and Live Nation. Much of the initial criticisms of the merger has been re-affirmed. Irving Azoff’s battles with rivals AEG (who are alleging antitrust violations) have been well documented, especially in regard to competition in the Los Angeles and New York City markets.

In a 2018 lawsuit, Radio Music License Committee made monopolization claims in a California court against Azoff’s Global Music Rights, LLC, a performance rights organization. They claim that the company is not being held to the same consent decrees as BMI and ASCAP. The matter is being investigated by the DOJ. It is claimed that the company is in violation of the Sherman Antitrust Act.

Controversy was generated when Azoff MSG Entertainment took part in a lawsuit against the city of Inglewood in an attempt to stop the construction of a new arena for the Los Angeles Clippers in Inglewood. The new arena would compete directly with The Forum which is owned by The Madison Square Garden Company. Another lawsuit from a local community group was filed to block the construction of the venue in June 2018. Inglewood mayor James Butts suggested that the lawsuit was brought about by “business interests from out-of-state”, suggesting that Azoff and the Madison Square Garden Company were using this group to ensure that they don’t have a competing arena nearby. The attempts to block the arena are similar to the tactics successfully used by the Madison Square Garden Company to stop the construction of the proposed West Side Stadium in New York City in 2005. That proposed stadium would have directly competed with Madison Square Garden. In December 2018, the LA Clippers sued the Madison Square Garden company alleging that they were trying to prevent the construction of a competing arena. During the summer of 2019, it was reported that Azoff was still working with James L. Dolan of the Madison Square Garden Company to prevent the competing arena from being built. Amongst the tactics being used to prevent the construction of the arena are lobbying efforts in the 2018 Inglewood mayoral election, financially supporting community groups which oppose the arena and helping to fund lawsuits seeking to prevent the arena’s construction.

In 2018, Nicki Minaj accused Azoff of orchestrating a smear campaign against her. Minaj alleged that Azoff contacted people in the media to say negative things about her and her tour. She had suggested that he had used his influence through Ticketmaster in a way that harmed her tour. As of 2019, Minaj is now managed by Azoff, which was announced on her Queen Radio Show.

In 2019, Azoff and his wife Shelli purchased The Apple Pan, one of Los Angeles’ oldest continuing operating restaurants. They also purchased Nate n’Al’s, founded in 1945, with a consortium of Los Angeles-based investors.

In March 2019, leaked emails revealed that Azoff attempted to lure the Los Angeles Lakers back to The Forum after their lease at the Staples Center was up. Despite nothing coming of the proposal, Azoff’s proposal to re-purpose The Forum was seen as a way of preventing the LA Clippers from building their own arena in Inglewood and ensuring that the Madison Square Garden Company got an unfair advantage over rival AEG, which already owns part of the Lakers.

In January 2020, Azoff was inducted into the Rock and Roll Hall of Fame as an Ahmet Ertegun Award winner.