Long-term heroin user Mosley, 39, was discovered slumped at his desk wearing only his boxer shorts and surrounded by drug-taking paraphernalia.
Mosley, who suffered from depression, died of cocaine intoxication, Westminster Coroner's Court heard.
Restaurateur Mr Mosley was discovered by his cleaner at his luxury home in Notting Hill, west London, on 5 May.
The inquest was told that Mosley started using drugs to cope with his shyness and admitted to his parents in 1994 that he had been taking heroin.
He sought the help of doctors to deal with the problem but habitually returned to drug-taking.
On the afternoon of 5 May, his cleaner, Samara Fadoti, found him at his desk on the third floor of his home wearing only his boxer shorts.
On the desk were crack pipes, syringes, needles and other drug- taking paraphernalia.
Miss Fadoti said: "I saw him sat at his desk - it was obvious he was dead.
"I screamed his name. I didn't know what to do."
The inquest was told that Mr Mosley attended a string of prestigious schools, studied maths at Oxford University and gained a PhD at the University of London.
After working in computing, he ran the successful and prestigious Hereford Road Restaurant near his home.
Coroner Dr Paul Knapman acknowledged that Mr Mosley enjoyed "a very promising start to life".
Recording a verdict of death by non-dependent drug abuse, he said: "Alexander Mosley was found sitting at his desk with his computer on, wearing boxer shorts only.
"Around the desk were crack pipes, syringes, needles, powders and things used for taking drugs.
"This is a tragedy for a man who, in so many respects, had so much potential.
"Unfortunately his propensity to return to taking drugs has caused his death at the age of only 39."
Toxicology reports found large traces of the by-product of cocaine in his system as well as much smaller traces of other substances including ketamine and morphine.
Mr Mosley's friend, Ramona Rainy, said she knew he had a history of using heroin and crack cocaine.
She told the court: "I was aware Al had been using hard drugs for many years and would often go missing for days at a time.
"I was aware that he had given up hard drugs for some time but had started to dabble again."
Miss Rainy received a missed phone call from Mr Mosley three days before his body was discovered.
Mr Mosley had last seen his father on the Saturday before he was found dead.
The two had enjoyed lunch together, with the restaurateur recorded as being in a "very enthusiastic mood".
The court was told that Mr Mosley was very active and was a keen skier and surfer.
His grandfather was Oswald Mosley, the former leader of the British Union of Fascists.
Max Mosley attracted international notoriety when the News of the World published footage of him in an S&M orgy with prostitutes.
But the 69-year-old was eventually awarded a record £60,000 in privacy damages against the newspaper last year.
None of Alexander Mosley's family attended today's hearing.
Mr Mosley had fought depression as well as a "long-term" addiction involving the abuse of heroin and cocaine, according to his doctors' reports.
His urine tested positive for cocaine, ketamine, MDMA (ecstasy) and heroin or morphine.
There was a large amount of the breakdown products of cocaine present, while other drugs appeared in trace amounts.
A post-mortem examination uncovered puncture-type wounds around Mr Mosley's elbows and groin.
Dr Michael Osborn, who performed the post-mortem, said it would have been "unusual" for such marks to have been caused by any medical intervention.
Harriet Hill, a lawyer for the Mosley family, pointed out that a shopping list was found, with reminders to deal with everyday items such as "plants, coffee, haircut".
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