Liz Murray's story of her journey from starving as a child in the Bronx to Ivy League success has become an American bestseller

A woman who overcame tremendous odds to go from "homeless to Harvard" has turned her life story into an American bestseller.

Liz Murray, 29, rose from some of New York's meanest streets to graduate from the Ivy League and has become an international speaker. But some of her earliest memories are of her parents spending their welfare payments on cocaine and heroin when she and her sister were starving: "We ate ice cubes because it felt like eating. We split a tube of toothpaste between us for dinner."

When she became homeless at 16, as well as stealing food she would shoplift self-help books and study for exams in a friend's hallway. Now Breaking Night: A Memoir of Forgiveness, Survival, and My Journey from Homeless to Harvard, has burst on to the New York Times bestseller list. Hailed as a "white-knuckle account of survival", it is to be published in Britain in January.

Born in the Bronx, Liz watched her parents mainlining coke all day. "Both my parents were hippies. By the time the early 1980s came around and I'd been born, their disco dancing thing had become a drug habit," she recalls.

She talks frequently about how much she loved them and how much they loved her, how they were highly intelligent but rendered hopeless at parenting by their drug dependence and consequent poverty. She remembers her mother stealing her birthday money, selling the television, and even the Thanksgiving turkey a church had given them, to scrape together money to score a hit of coke. Liz would turn up to school lice-ridden and was bullied for being smelly and scruffy and eventually dropped out.

Her mother's mantra was "one day life is going to be better", then she would spend all day throwing up and being nursed by her daughter or slumped in withdrawal, arms tracked with needle marks. When Liz was 15 her mother revealed that she was HIV-positive and had Aids. She died not long after and was buried in a donated wooden box.

When Liz's father failed to pay the rent on their flat and moved to a homeless shelter, Liz was out on the streets. Her sister got a place on a friend's sofa, but Liz slept on the city's 24-hour underground trains or on park benches.

At first she saw herself as a rebel and a victim, but then she had an epiphany. "Like my mother, I was always saying, 'I'll fix my life one day.' It became clear when I saw her die without fulfilling her dreams that my time was now or maybe never," she says.

She had nowhere to live and had not attended school regularly for years, but at 17 pledged to become a "straight A" student and complete her high school education in just two years.

She did a year's work a term and went to night classes. A teacher saw her gumption and mentored her. When he took his top 10 students to Harvard, she stood outside the university and instead of feeling intimidated she admired its architecture – and decided it was within her reach. Then she heard that the New York Times gave scholarships.

She graduated last summer. Oprah Winfrey gave her a chutzpah award and she met Bill Clinton. She has talked at events alongside Tony Blair, Mikhail Gorbachev and the Dalai Lama. She talks to teenagers about resisting the temptations of drugs and gangs. She also urges them not to use childhood hardship as an excuse not to take opportunities.

Her father died in 2006, also of Aids. His saving grace was that he encouraged her to read – and stole books from libraries to give her a love of literature.

She doesn't want her appearance now and her Harvard degree to fool anyone: "I was one of those people on the streets you walk away from."