The title of this posthumously published memoir might seem to presage an elegiac farewell to the good times. Musician, author, activist Gil Scott-Heron's untimely death, aged 62, in May last year, followed a decade filled with enough trials and tribulations, intoxication and incarceration to provide him material for several volumes bewailing the fickleness of life. But misery-lit this isn't, thank goodness.

Scott-Heron's final album (I'm New Here, 2010) opened with lines from his poem "On Coming from a Broken Home": "Womenfolk raised me and I was full grown/ Before I knew I came from a broken home." Some of The Last Holiday's most affecting writing fleshes out clear-eyed portraits of those strong females who nurtured him.

Born in Chicago in 1949, Scott-Heron was less than two when his parents separated. (His Jamaican father was a professional footballer who in 1951 accepted an offer to play for Celtic, becoming the Scottish club's first black player, known as the "Black Arrow".) A temporary stay with his maternal grandmother in racially segregated Tennessee was extended as she instilled in him the indelible joy of learning. At the age of four, Gil was devouring the columns of Langston Hughes in the Chicago Defender. She died when he was 12, at which point he moved north with his mother. He already knew so much about the random cruelty of death to be able to report: "I had run out of tears."

There are heart-rendingly honest revelations for psychologists to pore over: "Love was not an active verb in my family or in my life. There were few demonstrations, few hugs and embraces, and few declarations among us about love. I was a full-grown adult who had been married, a father, and divorced before I consciously put 'I love you' into conversations with my mother."

Yet this is a book with celebratory credentials. Scott-Heron's original intention was to produce a narrative in homage to Stevie Wonder's crucial role in pressing for the institution of Martin Luther King Day to be established  which finally happened in 1983. Wonder's 41-city tour across the US to promote his Hotter than July album, which features the irrepressible "Happy Birthday", was a pivotal point in the campaign. Scott-Heron opened each show of Wonder's tour, which culminated with an awe-inspiring concert and rally in January 1981 at the spot in Washington DC where King delivered his "I have a dream" speech.

By the time the book reaches this climax, we have seen why it mattered so much to Scott-Heron to be there. He has described the chequered education he collected through 17 years and 10 institutions; the social and political backdrop against which he developed his charismatic talents for literature, activism and music, recording his best-known song  "The Revolution Will Not Be Televised"  at the age of 21.

In an afterword, Jamie Byng, both the publisher and a long-time friend of Scott-Heron's, explains the book's long journey, with radical changes of structure and perspective along the way. That The Last Holiday has been published at all is something of a triumph, although tantalising loose ends about his personal life are destined to remain so. Towards the end Scott-Heron promises: "How I became a father again at nearly 50 years old is a story I will save for another time" Scott-Heron is undeniably a trickster wordsmith, reaching into his bag of goodies for turns of phrase and figures of speech that effortlessly hold attention. He veers from a slangy, conversational, wisecracking style to the tone of a perceptive philosopher, unable to resist mesmerising us with alliteration or suddenly dropping on us the sort of rhythmic street poetry that earned him the reluctant soubriquet "godfather of rap", equally able to evoke a mood of urgency or tenderness. The result is a riveting read that is, like its author, unpredictable and eccentric and funny and always compassionate.