The Caledonian Railway encouraged the Symington, Biggar & Broughton Railway to build a line towards Peebles, determined to reach the east coast of Scotland through the Borders. This objective was obstructed by the North British Railway, intent on dominating the Borders' railways. Eventually, the Peebles Railway was taken over by the NBR and the Caledonian swallowed up the SB&BR.

The SB&BR's extension to Peebles was authorised on 3 July 1860 but by the time construction was complete the company was part of the much larger Caledonian Railway. The Neidpath Viaduct, consisting of eight stone skew arches, was built to carry the branch line over the River Tweed, to the south-west of Neidpath Castle.

This very handsome structure remains extant, and crosses 9.8 m (32 ft) above the River Tweed obliquely on eight skew arches of ashlar blocks, each of 9.9 m (32 ft 6ins) span, with four of the piers in the water. The rusticated buttress pilasters are decorated with cruciform arrow slits and smooth angle margins extending from rounded cutwaters. The graceful curve of the line at this point had a radius of 402.4 m (440yds) in order to align the route with nearby Neidpath Tunnel, at the eastern end of the viaduct and to the south of Neidpath Castle. Cast-iron railings top the bridge, and signal cables having run along the parapets.

The bridge was designed by Robert Murray, a local architect living in Peebles, and George Cunningham, Consultant Engineer to the Caledonian Railway. The similar, but smaller, Lyne Viaduct is located a little to the west and is often confused with this bridge.

On 1 January 1923 ownership of the viaduct, along with the rest of the Caledonian Railway, passed to the London, Midland and Scottish Railway and thence to the Scottish region of British Railways on nationalisation in 1948. The line lost its regular passenger traffic on 5 June 1950 and closed completely on 7 June 1954.

This Category A listed structure, one of the finest examples of skew arch construction in Scotland, is now in use as part of a popular footpath.