THERE is no other botanic garden in the world, so the Inverleith House curator Paul Nesbitt tells me, with an award-winning contemporary art gallery tucked in amongst the rhododendrons. In this utterly unique combination, the capital has something which is much more than the sum of its substantial parts.

For thirty years now, Inverleith House, under the direction of its curator Paul Nesbitt, a man with both botanic and artistic credentials, has been showcasing contemporary art in the airy surrounds of this Georgian house which, in a previous incarnation was the founding home of the Scottish National Gallery of Modern Art. Its diverse roster since 1986 has ranged from Andy Warhol to Agnes Martin, John Cage to Stanley Kubrick, Ian Hamilton Finlay to Cathy Wilkes, Ciara Phillips and William Eggleston.

The premise has been straightforward, says Nesbitt. Invite artists who haven’t had a major public show in Scotland – or even the UK – before, and give them the opportunity. “What’s the point in showing someone everyone else has already shown?” he says, as we wander around this joyous and engrossing thirtieth anniversary exhibition, part of the Edinburgh Art Festival, containing work from selected artists that have shown over the past thirty years. True to the gallery’s central thesis, a good portion of the work has either not been shown here before, or is new.

If Inverleith House is a major contemporary art gallery, it is not one divorced from its surroundings. Artists frequently use the unique situation of the gallery in the Botanics, and indeed are very much attracted to working there, to reframe their own work and the gardens outside, viewed through the tall and perfectly proportioned Georgian windows. The result is exhibitions which throw into relief the botanical context in which they are found.

Even on a dull day, the quality of light in the house is exquisite. On the ground floor, bright “botanical” landscapes by Nicholas Party provide an alternate reality to the gardens outside. Elsewhere, Marc Camille Chaimowicz’s colour-saturated drawings are installed in the same place as they were during his 2010 exhibition exploring the house’s domestic past.

There is a lightness here, and much to delight. Dan Colen’s whoopee cushions – in blown glass or cement-filled – lie on the floor, terribly tempting and a small reminiscence of his rather joyous 2013 exhibition, The Illusion of Life. There are new works too. Karla Black, who represented Scotland at the Venice Biennale in 2011 and in the same year was nominated for the Turner Prize, has made a plastic "cloud" sculpture, daubed in green paint, hung airily over the window. Cerith Wyn Evans’ Dear Lucifer (2009) has been reinstalled here, three mirrored plinths, reflecting, dissembling, and topped this time round with a cactus and a very healthy-looking orchid (this is the Botanic Gardens, after all). Reflected from the wall behind, Roni Horn’s Remembered Words draw the eye, free associating between words.

The gallery’s kudos amongst artists is clear. Here is a sketch by Andy Warhol from the 1952, an unidentified portrait of one of his many acquaintances, first exhibited here in 2003. Here is a neon Ian Hamilton Finlay, ICI on Danse, slowly pulsing its message on the wall. Here is a sculpture by Louise Bourgeois, the pink marble Topiary, originally exhibited in 2009 alongside her works on paper and historic botanical images made in the 19th century for John Hutton Balfour.

Indeed, key historical works from the archive are the focus of two central rooms in the exhibition, containing superb images from the botanical drawing archives, collated, collected and teased out of the Herbarium over the past decades through the assiduous research of Henry Noltie, who single-handedly identified and drew together the Indian botanical drawing collections (Hugh Cleghorn Collection, 1820-95) from half a million drawings in the archive.

In a glass case in the basement, reminiscences and notes from backstage, snapshots and letters to the curator from John Cage, Merce Cunningham and others. The air of celebration is palpable, but the future is uncertain for Inverleith House. Alongside many other important arts organisations, the gallery lost its Creative Scotland funding last year. Whatever the future holds for this gallery – and one sincerely hopes it continues to develop within its contemporary remit – this cannot be Inverleith’s farewell. Miracles, here and elsewhere, are needed.

I still believe in miracles…, Inverleith Gallery, Royal Botanic Gardens, Edinburgh to October 23

www.rbge.org.uk