Whatever the cause, it happened a long time ago: the 35-metre specimen is the oldest tree in one of the world's great arboreta, Dawyck Botanic Garden. It was planted by the then owners of the estate, the Veitches, in 1680 – just a year after the duke of Monmouth's forces had crushed the Covenanters at the Battle of Bothwell Brig, and nine years before Graham of Claverhouse would lead the first Jacobite uprising.

"It must have seen a lot in its time," says Graham Stewart, garden supervisor at Dawyck, which these days is one of the specialist outlying gardens of the Royal Botanic Garden Edinburgh. There are several such majestic "heritage trees" in this superb collection of North American and European conifers, but a new chapter in its history will begin on Wednesday, when Richard Lochhead, cabinet minister for the environment, opens a £1.3 million visitor centre there.

Clad in glass, timber and distinctive bronze panelling, the low-lying, eco-friendly building features a flat roof, layered with a rich mat of sedums as insulation, and it runs on a woodchip-fuelled biomass boiler. With its airy café, shop and exhibition studio, and expanded plant sales facilities, the centre is a marked change from the comfy but cramped conservatory-with-tea-counter that used to act as reception at the garden.

Dawyck is the first of the RBGE gardens to open a bespoke visitor centre – the main Edinburgh garden's much heralded Great Gateway, currently under construction, will open next summer – and Stewart welcomes the new building, designed by the Edinburgh architects Simpson & Brown.

"I think it is much more reflective of what the garden should be offering in terms of a restaurant facility and also the studio," he says.

"There is now big potential for us to expand. With the previous centre, our visitor numbers had pretty well stagnated at round about the 20,000 to 22,000 mark. The problem wasn't really the garden, which can cope with any number of visitors, but the old conservatory was limited and on busy days it just wasn't working."

The garden's situation, almost as far from a coast as you can get in Scotland, means it has a very different climate from either the Edinburgh garden or its two other satellites – the mild, damp Benmore in Argyll and the sub-tropical Logan in Galloway. The slopes that flank the Scrape, a tributary of the nearby Tweed, enjoy a climate that is virtually continental.

Dawyck therefore suits hardy plants from colder, drier parts of the world, and of particular importance is its collection of conifers from North America and elsewhere, such as the aforementioned silver fir, a European larch planted in 1725 and some magnificent giant redwoods and Douglas firs established in the mid-19th century. The garden also boasts its very own beech cultivar – the Dawyck beech (Fagus sylvatica "Dawyck"), a strangely narrow and upright but elegant fastigiate form descended from an original sapling found growing in a local wood in the 1800s and transplanted to the estate.

Three visionary planting families made Dawyck what it is today during their ownership over three centuries: the Veitches (who introduced the first exotic tree species, the horse chestnut, to Scotland); the Naesmyths; and the Balfours. Some of the European larches here were reputedly planted in the early 18th century by Sir James Naesmyth with the Swedish botanist and classification pioneer Carl Linnaeus, while it was Colonel Alastair Balfour who gifted the garden to the nation in 1979.

Many of these trees and shrubs also stand as memorials to doughty plant hunters who often underwent privation and danger to collect them, such as Ernest "Chinese" Wilson (1876-1930) and the earlier David Douglas, after whom the mighty Douglas fir is named. In fact, the garden features a David Douglas Trail dedicated to the Scone-born plant hunter.

But Dawyck is not all history. Like other RBGE gardens, it has an important research and conservation role, and high on its hillside, flanked by native beech woodlands, you will also find perky, mesh-guarded saplings of Sicilian fir, endangered in their native land and under cultivation as part of the RBGE's International Conifer Conservation programme. In recent years, on the upper slopes near the old Dawyck chapel, a Nepalese garden has been established, with the gleaming white bark of the Himalayan birch and prayer flags fluttering from one tree – a legacy of Nepalese students who have spent time here.

Dawyck is more than an arboriculturalist's paradise, however. February to March sees the banks of the Scrape Burn starred with snowdrops, there are currently swathes of daffodils, while bluebells should be laying a pastel haze for this month's ministerial opening. An important collection of hardy rhododendrons provides plenty of colour along the Italianate urned walks and terraces into the summer. At the moment , the distinctive yellow "candelabra" flowers of the bog-loving North American skunk cabbage (Lysichiton americanus) are clustered by the burnside, while in June blue Meconopsis poppies will bloom in the lower glen.

In almost perverse contrast to Dawyck's forest giants, three and a half hectares of its beech and pine wood have been designated as the world's first Cryptogamic Sanctuary, where fallen trunks and boughs are to left rot and support "lower" plant orders such as fungis, mosses, lichens, liverworts and ferns in a unique field laboratory.

It is trees, however, which give Dawyck its character, and it is perhaps fitting that the opening exhibition in the new centre's studio is devoted to the legacy of the late Tim Stead, whose self-confessed "amazement" at trees and the artistic potential of their timber inspired his revolutionary approach which, as the exhibition states, "not only blurred the lines between sculpture and furniture design, but extended into conservation, business philosophy and teaching".

Stead, who had a longstanding relationship with the RBGE, died in 2000. While the exhibition includes some of his own distinctive chairs and wonderfully neolithic-looking interlocking and chambered artefacts, the new centre's café sports a suite of tables and chairs from his continuing workshop at Blainslie, and it is hoped – funding permitting – to expand this, using fallen timber from Dawyck itself.

For further information, visit www.rbge.org.uk/the-gardens/dawyck