In June 2010, David Servan-Schreiber was diagnosed with a malignant brain tumour. He was 49. It wasn't his first – he had survived one in his early 30s. This time he wouldn't be so lucky. The cancer was aggressive and his decline swift. He died 13 months later, last summer.

David was a doctor, a celebrated psychiatrist and neuroscientist, but after the first brain tumour, he made cancer his life's work. His mission was to tell people that by making a few simple lifestyle changes they would have a far better chance of staying well. He wrote two bestselling books about his ideas that were translated into 35 languages.

But nothing could help him stave off his own cancer this time.

As a physician, David had seen at first-hand how squalid – and lonely – death could be for many people. He wanted to make sure he had "a successful death experience" – and to write one last book that might help others do the same. He wrote Not The Last Goodbye in April and May of this year, and it was published in his native France in June. It went straight to the top of the bestseller lists – just in time: David died on 24 July.

"He wrote the book, I think, to give meaning to what was happening to him," says his brother, Emile. "Being a terminally ill patient is something that affects everyone who has to go through it with you – in other words, your family. He wanted to use his experience as a patient himself, but also as a doctor, to show how we can all go through this process with as much dignity as possible – how to be afraid, yes, but also courageous."

David was the eldest son of Jean-Jacques Servan-Schreiber, a French journalist and politician. The family moved from Paris to America in the mid-80s, where the four brothers attended the University of Pittsburgh, to which David would later return as clinical professor of psychiatry.

"We were always very close," says Emile. "We were four boys together – no girls – with a very present father who treated us like his little army."

Weren't they very competitive? "No, we were always too tight for that."

The boys remained close into young adulthood, then went off to forge their careers: into business, entrepreneurial start-ups and, in the case of Emile, cognitive science. David, meanwhile, became a celebrated psychiatrist. He was one of the founders of the American branch of the medical charity Médicins Sans Frontières and served as a volunteer director in various countries around the world. In 2002, after receiving the Pennsylvania Psychiatric Society Presidential Award for Outstanding Career in Psychiatry, he turned to writing the self-help books that would find huge global audiences.

In 2005, Healing Without Freud or Prozac set out a drug-free approach to treating stress, anxiety and depression. In 2007, Anticancer: A New Way of Life was designed to help readers reduce the chance of developing the disease by describing the preventive regime he adopted after surgery, chemotherapy and radiotherapy for his first tumour.

His success, driven by a workaholic tendency, took an inevitable toll on his private life. He divorced his first wife, with whom he has a son, Sasha, now 15. Even when he got married a second time – to Gwenaelle, who he says taught him how to love, and be loved, for the first time – he admits in the book that it was hard to slow down, and to always practise what he preached.

Having spent years helping patients prepare to die, David now had to face his own end. "Perhaps it is a good exercise to work out what we would say to our children if we knew we were about to die," he writes. "With my elder son, Sasha, I'm happy to say I've talked about it openly. [But] the fact that he lives far away [in America] has long been a source of suffering for me."

He explained to his son that he didn't know how much longer he had; perhaps Sasha and his mother could consider returning to live temporarily in France? Sasha replied, both directly but enigmatically, that it was hard having a sick father. His father relented. "We wept together."

The book is only 136 pages long, economical in tone and to the point. It is unflinching in tackling some of the biggest issues we face in life, but it is only when he talks about his wife, and children, that his prose becomes wistful and emotional. At one point, he dwells on the paternal absence his passing will have, and mentions a soldier from the American civil war who wrote to his wife before leaving for battle, convinced he would not return.

"[And] if he didn't, he hoped that every time she felt a breeze on her face, she would know he was there. I would like to share that image, that intuition, with my wife and children, so that when they feel the gentle caress of the wind on their faces, they can say: 'Hey, it's Dad, come back to kiss me.'"

He also uses the book to extol the importance of the family unit. So that he didn't just have to rely on Gwenaelle who was then pregnant with their second child, two of David's younger brothers promptly gave up their jobs to become his full-time carers. This must have been a considerable sacrifice. "Perhaps," says Emile. "But we are certainly not the only family to do so. It's an experience that cannot be taught. You just have to live through it and learn, and cope, the best you can."

Calls were also put out to extended family members, his many uncles, aunts and cousins scattered throughout France, all of whom made prompt pilgrimages to David's bedside.

"The whole family came together and we lived through it all together, not as something horrible – although of course it was – but as something we could share," says Emile.

David spent his final months in a hospital room crowded with well-wishers. There were many all-night vigils. David, the empathetic doctor, strove to keep the mood light, and encouraged those closest to him not only to come and say a final goodbye, but, should he still be alive the following week, to come and say goodbye again. He spent as much private time with his wife as he could, and with his two younger children, Charlie, then aged two, and Anna, who was six months, keenly aware that they would grow up with no physical memory of him. He had planned, says Emile, to leave a series of video messages for the children, but never quite had the energy: "What he did have, he wanted to use writing his book."

Emile wrote the moving epilogue to Not The Last Goodbye, about his brother's courage. "Those of us who had the privilege of taking care of him, of accompanying him in his ordeal, often had the feeling that it was he who was taking care of us. He would meet our clumsiness with limitless patience; he would dissipate with a grateful gaze any embarrassment caused by his extreme physical dependence on us. David was not afraid of death. He believed it would transport him to a kingdom of love, through the famous tunnel of light so often described by those who have had a near-death experience. May it be so, my brother."

David died as he hoped he would, with his family by his side.

"That was important to him," Emile says. "David made sure that it was a very connected time for us all. It was something he cared about a lot, and he remained connected to us all until the very end. That was his way."

• Not The Last Goodbye: Reflections on Life, Death, Healing and Cancer by Dr David Servan-Schreiber is published by Pan Macmillan, £12.99. To order a copy for £12.49 with free UK p&p, go to theguardian.com/bookshop or call 0330 333 6846