Born in Baku, Agalarov was educated at the Azerbaijan Polytechnical Institute. There, he studied computer engineering and was a member of the Communist Party of Azerbaijan and Baku City Committee. He moved with his family to Moscow in 1998, where he co-founded Crocus International alongside his father-in-law, Iosif Yevgenevich, which specializes in trade fairs, where he still makes most of his money.

In 2012, the Crocus Group (ru) built a new campus for the Far Eastern Federal University outside Vladivostok. Agalarov says he had to buy a larger Gulfstream jet to visit the site, where he spent $100 million of his own money on cost overruns on the $1.2 billion campus of 70 new building on Russky Island overlooking the Pacific Ocean. He then won projects for a Moscow superhighway and two stadiums for the 2018 FIFA World Cup.

In January 2013, Agalarov and his son visited Las Vegas, Nevada, after Donald Trump, the beauty pageant's owner, announced at Miss Universe 2012 that the next competition would be hosted by Agalarov in Moscow. He paid Trump $20 million to host the pageant. In November 2013, President Vladimir Putin awarded Agalarov the Russian Order of Honor. That month, Agalarov hosted Miss Universe 2013 at his Crocus City Hall.

In 2014, Kyrgyzstan signed a treaty with Russia that named Crocus Group as the single supplier of services to integrate into the Eurasian Economic Union, avoiding competitive bidding on the $127 million deal.

Agalarov is married and has two children. His son Emin Agalarov is a businessman and singer/songwriter. Emin was married to Leyla Aliyeva, the daughter of the current President of Azerbaijan, Ilham Aliyev, until they divorced in May 2015. Agalarov has twin grandsons from his son's marriage.

Agalarov's son, Emin, helped arrange Russian Lawyer Natalia Veselnitskaya's June 9, 2016 meeting with Donald Trump Jr., Jared Kushner, and Paul Manafort in Trump Tower. Emin says that after Trump won the United States presidential election in 2016, Trump sent them a handwritten note, saying he does not forget his friends.

As of June 2017, he had an estimated net worth of US$1.91 billion, most of which is derived from his real estate ventures. In January 2017, Forbes listed him as the 51st richest Russian.