In 1982, Shirley Hazzard flew to Britain for a reunion with Alec Vedeniapine, a man with whom she had been in love more than 30 years before. Vedeniapine and his wife farmed in Wales, and their world – cats and cows; damp, rural isolation - couldn’t have been more different from that of Hazzard, who lived with her husband, Francis Steegmuller, a biographer of Cocteau and Flaubert, on New York’s Upper East Side in an apartment filled with paintings by Matisse and Picasso. Yet the contrast only made her feelings for Vedeniapine the more categorical. The considerable achievements of her own life were, even now, to be measured (favourably) against her sense of what she felt he had “renounced” all those decades ago. Carefully closing her eyes to the existence of his family, she found herself struck by “this theme – this transcendent theme – of fulfilment and non-fulfilment; and those who bind themselves to limitations”. Though the two of them would stay in touch, they did not meet again.

As I’ve written it, this may sound unkind, cold to a degree. In fact, the opposite is true. Hazzard’s judgments – in life, as on the page – were born of a deep intensity of feeling; a sensitivity that was unfashionably romantic. She and Vedeniapine had fallen for each other in postwar Hong Kong, only to be separated when Hazzard, then still a teenager, had to follow her parents to New Zealand, a move made for the sake of her sister, who was ill with tuberculosis. But the memory of their broken engagement – ended by Vedeniapine in a letter – would stay with her for ever, underpinning all that she wrote. Love between two people, she believed, is never a small thing. It may be frangible, the victim of fated misalignments, but its mark is permanent. The abiding themes of her marvellous novels – there are just four, of which the most celebrated is The Transit of Venus, published in 1980 – are love and destiny; devastation, for her characters, is always around the corner for the simple reason that vast and unseen forces are working unceasingly to impede love’s bliss and power, its ineffable ability to change everything in a stroke.

Brigitta Olubas’s new biography of Hazzard runs to more than 500 pages and I must admit that I approached it with trepidation. Olubas is an academic at an Australian university and her subject’s life was, to a large extent, inward: a writing life, above all. It seemed impossible that she would be a good match for a storyteller who gives her readers (passionately devoted, but still far too few in number) access to the most grand of emotions; whose husband said of The Transit of Venus: “No one should have to read it for the first time.” There would, I assumed, be jargon of the kind that Hazzard, an autodidact who disliked modernism in most of its forms, would have loathed.

But it turns out that I was wrong. A friend of the intensely social Hazzard once remarked that she made those around her seem better to themselves – women, said the critic Alan Pryce-Jones, “got more good looking in her presence, or put on their individuality” – and perhaps she has had an effect on Olubas, too. In her company, Olubas has developed an enviable tenderness; a way of linking her subject’s life and work that is both unobtrusive and unerring. This is a fascinating, searching, compassionate book. It moved and transfixed me. More importantly, it has sent me back to Hazzard’s writing, which is so good I don’t think I could love someone who didn’t also adore it.

She comes with a certain elusiveness. The curious timelessness of her novels is matched by the sense that, because she is from everywhere, she’s also from nowhere. The story of Hazzard, an Australian who disdained the butch, rather philistine world into which she was born in 1931, is one of self-invention, of smoothing your corners with voracious learning and civilised company. But Olubas is good on all of it, carefully contextualising the Sydney roots; the influence of her travels, courtesy of her father’s job as a trade envoy, to Japan, where she saw a ruined Hiroshima, and thence to Hong Kong, London and New York; the powerful need to separate herself from her warring, needy parents. In New York, Hazzard worked in a lowly capacity – filing and typing, mostly – at the United Nations, an institution that would come to preoccupy her nonfiction (she was a relentless critic), but which also, Olubas concedes, saved her. Fleeing yet another failed love affair with an older, married man, she was posted to Naples. Embraced by a well-connected family, the Viventes, she was at last “released” into “a larger life”. Thereafter, Italy would always give her the feeling of home.

Back in New York, she began writing stories for the New Yorker, becoming a lifelong friend of her editor, William Maxwell. It was, however, through another writer, Muriel Spark, with whom she later fell out, that she met Steegmuller. When they married, she was 32 to his 57. Steegmuller was wealthy and well connected; he could – she saw this clearly – end her precarity. But he was also extremely refined and “with Taste itself, honed through assiduous application, so essential to both”, they embarked on what would be a fine life together. They rented apartments in both Naples and Capri, shipping their Rolls-Royce to Europe to be driven in the months when they were there. They went to the opera, and to galleries, and read all the right new books. They knew John Cheever and Alberto Moravia, Harold Acton, Bruce Chatwin and Graham Greene. Hazzard wore Missoni and Ferragamo.

All this is quite perfect. Absorbing the glamorous details, I felt like the Frenchman who, in a signing queue, told Hazzard delightedly that she looked to him exactly as she should. But it’s for her heart and her mind that you really read this book, in my case in two greedy, exhausting sittings. Olubas brings you close to both and it is exciting and painful. Exciting because Hazzard was a genius. Painful because she is gone and left relatively little behind. Exciting because she knows you better than you know yourself. Painful because that self is so wanting. Not just less clever and sophisticated than her, but less demanding and expectant, too: hopelessly bound to your limitations.

• This article was amended on 17 May 2023. “No one should have to read it for the first time” was a quote about The Transit of Venus, not The Great Fire as an earlier version said.

• Shirley Hazzard: A Writing Life by Brigitta Olubas is published in the UK by Virago (£25), and in Australia by Hachette ($34.99). To support the Guardian and Observer order your copy at guardianbookshop.com. Delivery charges may apply