One of the most persuasive candidates for the title of Godfather of Rap, a musician who could hold his own in the most illustrious of jazz company, a writer of some of the most incisive political music to come out of the US, a wordsmith whose talents encompassed novels as well as poetry and song lyrics, and a committed political activist, Gil Scott-Heron is still regarded with particular fondness round these parts because his father played for Celtic FC.

My impression was that he became just a little fed up being asked about that every time he set foot in Scotland, but the tale is fully told here – and it would have been understandable if the musician had declined to talk about it all.

Gil Heron senior, a Jamaican who had served in the Canadian Air Force, abandoned his wife and baby son in Chicago when Celtic came calling in 1950, offering the chance to play professionally. Although Scott-Heron does not blame his father for grabbing the opportunity, he is equally clear that dad's decision shaped the future course of his life. He was subsequently raised by his grandmother in Tennessee, and then lived on the breadline with his mother in New York City. His father presumably did not get the best of press at home. "There was no real incentive to maintain concern about him ... He just wasn't important," he writes. "So imagine my surprise when I arrived at a place where he was important."

Scott-Heron then recounts the publicity work he did to help boost slow sales for a concert in Glasgow in the 1970s (the Edinburgh date was doing fine) in partnership with the Celtic captain his father had played alongside, and his crash course in the politics of the Old Firm. Quick on the uptake, and no stranger to sporting loyalties back in the States, he appeared on television sporting a Celtic scarf – and a Rangers hat.

Truth to tell, I did not expect to find this much local interest in The Last Holiday, although Gil Scott-Heron made fairly regular visits to play in the country that apparently nicknamed his father "The Black Arrow". The holiday of the title is Martin Luther King Day, which was established in the 1980s following crucial campaigning work by Stevie Wonder, whose Hotter Than July Tour, Happy Birthday single and Washington DC rally on January 15, 1981 were all dedicated to that end. After Bob Marley's illness forced him to pull out, Scott-Heron was the support act.

There are indeed a number of chapters recounting the events of that tour, including a description of the star quality, talent and charisma of Michael Jackson, who added his considerable cultural weight to the effort at the Madison Square Garden date, which is among the best writing in the book; but in some ways (particularly the amount of superfluous detail they contain) they are the weakest chapters.

At some point, and encouraged by Canongate's Jamie Byng, who had republished Scott-Heron's early pre-music-career novels, the memoir expanded to embrace the back story of the author – the reason, if you like, why Martin Luther King Day and Stevie Wonder's work to have it made a public holiday, were so important to Gil Scott-Heron.

The result is a book that starts with the families of his parents (and especially that of his beloved mother) and progresses through his own young life, explaining how he stumbled into a musical career. It is the story of a young man of the first generation to really reap the benefits of the civil rights movement – and who was properly grateful for that and keen to build on the work.

The style of these early chapters is a delight, full of wit and alliteration and studded with passages of verse. It is social documentary with comment, a skill that Scott-Heron demonstrated in his great songs: The Revolution Will Not Be Televised, Home Is Where The Hatred Is, The Bottle, B-Movie and Johannesburg. And if for no other reason than the fact that these were groundbreaking classics, we should be interested in the life-story of the man who made them. That he is such great company on the journey is a bit of a bonus really.

But then this entire book is just that. Gil Scott-Heron died in May of last year, barely into his 60s and just embarked on his latest creative resurgence with the album I'm New Here, which had been the subject of a hip remix project. In an afterword, Byng explains the somewhat fragmented creation of the book now published and gives considerable credit to editor Tim Mohr for its eventual shape. His triumph is that the voice of Gil Scott-Heron is unmistakable, as anyone who saw him live will recognise.

This is no more movingly true than in the post-Stevie Wonder chapters, where he deals with his own declining health and the death of his mother. In the final pages he clears her house and meditates on his own (and his family's) inability to express love, ending with the most downbeat conclusion. It is a heartbreaking read as the last testament of a much-loved man, but it should certainly be read.