"It's a completely new way of making sculpture. It's amazingly moving. It's not only shocking but (also] very beautiful. I thought it was important for Scotland to have this piece; you can't drive around Scotland without having a sheep crossing the road in front of you."
Modest but plainly delighted, D'Offay walks through the Scottish National Gallery of Modern Art, where part of his extraordinary collection, built up over his career, is going on show. D'Offay took the art world by surprise in 2001, when he announced his retirement at the age of 62. Talks were announced in 2006 between the Tate and the National Galleries of Scotland to buy the collection, with the deal finalised in 2008. From tomorrow, the work of Hirst, Andy Warhol, and three other striking modern artists is on display as part of Artist Rooms. It is the first Scottish opening in a nationwide roll-out of art from the 700 pieces and 31 artists in the D'Offay collection.
The National Galleries of Scotland and the Tate Gallery jointly bought D'Offay's art collection last year for 26.5 million – a fifth of its estimated current market value – in what was described as a great act of public philanthropy by the renowned art dealer. More exhibitions follow in Glasgow, Orkney, Inverness, Aberdeen and 13 other UK cities across the UK.
"The collection catapults us into the international league," says Simon Groom, the director of the Scottish National Gallery of Modern Art. "It's a great day for us. It consolidates our position as one of the major galleries of Europe, with a substantial international collection, at a time when most of the artists in it are unaffordable."
Hirst's work fills four rooms and dominates the show, which occupies the prime ground-floor space of the gallery for six months until November, double the length of a typical run. Entry to the exhibition is free as D'Offay has insisted it should be from the start.
The goal is to let school and student groups, as well as Scotland's summer tourist crowd, receive the full benefit of having the top names in contemporary art brought to their doorstep.
Hirst's favourite theme – life paired with death, as opposite and partner – runs through not only his own works but also those by other artists in the collection. An early photograph, With Death Head, shows him posing as a 16-year-old with his own perky, teenaged face alongside a grisly, freshly severed head in a Leeds morgue.
The first room of the Edinburgh show is devoted to the work of the American photographer Francesca Woodman. Her camera was turned mostly on herself – nude, hiding behind an umbrella, shadowed by a door, or strangely blurred.
"Bunny bun I'm in the photograph come fetch me if the mood or a rock should strike you," she has scrawled underneath one of the black-and-white pictures. It was inscribed to her boyfriend, Benjamin Moore.
Woodman took her own life in 1981, aged just 22. Her photographs have gained international fame, but her early death gives them a particular poignancy.
"She is increasingly becoming more well-known, but within photographic circles her name has been well-established for some years," says Lucy Askew, the managing curator of Artist Rooms.
The opening tour of the D'Offay rooms is financed by 175,000 from the Scottish Government and 250,000 from the Art Fund. In Scotland, exhibitions of artists ranging from Robert Mapplethorpe to Ron Mueck are opening in Glasgow, Inverness, Orkney and Aberdeen.
The works "show Scotland as a serious player on the international cultural stage", says the culture minister, Mike Russell. "It offers an opportunity to inspire and influence a new generation of artists… This collection will reach our communities across the country giving them unparalleled access to the very best of modern art."
While Hirst's works are owned by galleries and collectors across the world, the Artist Rooms show marks the first time in Britain the artist has got the full museum treatment, gallery staff say. The works range from his medicine cabinets to spin and spot paintings.
Something for Nothing is a series of glass and mirrored cabinets that run to head height. On one side, 32 fish hang in formaldehyde-filled cases as if caught mid-stream, while on the other side, fish skeletons are suspended.
Transporting Hirst's work is a high-maintenance operation. The work arrived in Edinburgh in 17 boxes, to be reassembled with painstaking care. Oxygen that built up in the tanks during the journey had to be bled out and the formaldehyde solution topped up.
Likewise, the sheep arrives separate from its container and has to be reinstalled in its tank, with a London team arriving to do the job over two or three days.
"It's quite a business, but the final result is an amazing thing," says Phillip Long, the National Gallery of Scotland curator for Artist Rooms.
The Artist Rooms tour centres on international artists that D'Offay worked with, sold and collected in his long, London-based career as an art dealer.
In Edinburgh and across the country, the galleries are using the richness of the D'Offay works to draw in other loans – Something for Nothing was lent by another private collector. D'Offay himself is negotiating to add an additional work from the painter Alex Katz – a table sculpture of painted portraits – to make a stronger "room" in Orkney. Also in Orkney, the video artist Bill Viola is lending a new piece to the D'Offay exhibition of his work.
The uncompromisingly contemporary, life-and-death feel of the Edinburgh exhibition continues with Andy Warhol's stitched photographs – identical photographs sewn together, playing to Andy Warhol's familiar style of repetition and reproduction. They include Dissection Class, with a hanging corpse that is being dissected next to a skeleton, and Cadaver, featuring more grisly body parts.
The work of Vija Celmins, in sharp contrast to Warhol's mass reproduction, shows an artist labouring over finely detailed pencil drawings of stars and sky, or intricate woodcuts of the sea. Ellen Gallagher's paintings and Pop Art-style collages explore her own African American origins, and popular "black" images from skin-whitening to minstrel make-up.
Away from the Flock was first created in 1995; there now exist three different versions of it. It's the way Hirst presents his specimen – in a lifelike pose, in a simple cast, solitary, forcing a viewer to reflect upon it – that is said to carry power.
"It's a new way of looking, invented by Damien," D'Offay says. "When you look at Away from the Flock, you are looking at something that is going to be in all the history books."
• Artist Rooms is at the Scottish National Gallery of Modern Art from tomorrow until 8 November. Other works will be shown at: Tramway, Glasgow, 17 April-31 May; Inverness Museum and Art Gallery, 26 April- 27 June; Pier Arts Centre, Stromness, Orkney, 19 June-5 September and the Aberdeen Art Gallery, 29 August-31 October. For details, visit: www.nationalgalleries.org/artistrooms