The water beneath the bridge is called Caolas Cumhann - Gaelic for 'narrow strait', pronounced approximately 'Kyles Cuan'. It connects Loch Glencoul and Loch Glendhu inland with Loch a' Chairn Bhain that opens onto the Minch. The channel is about 120 metres wide and up to 25 metres deep, which produces fast tidal currents that change direction four times a day. The ferry that the bridge replaced ran about 400 metres east of the present bridge site, between the small villages of Kylesku on the south side and Kylestrome on the north. In rough weather or at peak tides, the ferry would stop. For a remote part of Sutherland with no alternative road, this was a recurring problem.

In June 1978 Highland Regional Council asked Ove Arup & Partners Scotland to study whether a bridge made sense. By March 1979 the feasibility study was complete. The engineers settled on a curved concrete box girder design with V-shaped inclined piers. The curve allowed the approach roads to follow the contours of the land rather than carve new cuttings through the hillsides. The V-shaped piers - eight inclined legs in total - reduced the length of the main span and balanced their lateral forces so that the total force on the foundations pointed straight down. The bridge is 276 metres long with a 79-metre main span. The deck sits 24 metres above high water to give navigation clearance for ships entering the lochs. The legs are reinforced concrete, the deck prestressed concrete tensioned to forces up to 52,200 kilonewtons.

Approach roads cost £4 million and began in summer 1981. The bridge itself started in August 1982. The main contractors were Morrison Construction and Lehane, Mackenzie and Shand. The total bridge cost £4 million against an initial budget of £2.75 million - an overrun of about 45 percent, modest by the standards of public works of that era. Construction had to deal with high winds, fast tidal currents, and the practical challenge of casting curved sections over deep water in a remote part of Scotland. The bridge opened to traffic in July 1984. Queen Elizabeth II formally opened it on 8 August 1984.

In 2019, Historic Environment Scotland did something unusual: it Category-A listed a bridge that was only 35 years old. Category A is the highest grade of architectural protection in Scotland, normally reserved for buildings of national or international significance. The citation called Kylesku 'visually striking and technically innovative' - rare praise for late-twentieth-century infrastructure. At the same ceremony, the bridge was officially renamed by its Gaelic title, Drochaid a' Chaolais Chumhaing. The listing recognises something the engineers had aimed for from the start: that a bridge designed to be sympathetic to its setting could, after a generation of weathering, become part of that setting rather than an intrusion on it. Today the curve is one of the iconic images of the North Coast 500 driving route, photographed thousands of times each summer.