The bridge was built in the 19th century, in the neoclassical style as the medieval city was modernised and expanded to the north and east.

In the early nineteenth century, the inconvenient access to Edinburgh by the great London road had long a subject of general regret. To enter the city from the south, the route ran through narrow and inconvenient streets, an approach that was considered unsuited to the general elegance of the place. In 1814, however, a magnificent entrance was commenced from Calton Hill to Princes Street over a deep ravine called Low Calton that was then occupied by old and ill-built streets. To connect Carlton Hill with Princes Street, all these streets were swept away, and an elegant arch, called Regent Bridge, was thrown over the hollow, making the descent from Carlton Hill into Princes Street easy and agreeable.

Inscription on the north side of Regent Bridge

Sir John Marjoribanks, the then Lord Provost of Edinburgh, presented the plan to build Regent Bridge to the City magistrates on 1 March 1814 with a projected cost of about £20,000 and backed up by a feasibility study by the engineer Robert Stevenson. This project was accepted and the bridge was designed by Archibald Elliot. Construction under the direction of Robert Stevenson began in 1816 and the bridge was finished in 1819. It is a major example of Greek Revival architectural work of the time. The arch is semicircular, and fifty feet (15.24 m) wide. At the north front it is forty-five feet (13.716 m) in height, but at the south front it is sixty-four feet two inches (19.558 m), because the ground declines to the south. The roadway is formed by a number of reverse arches on each side. The great arch is ornamented on the south and north by two open arches, supported by elegant Corinthian columns. The whole property purchased to open the communication to the city by this bridge cost £52,000, and the building areas sold for the then immense sum of £35,000. The street along the bridge was called Waterloo Place, as it was laid in the year on which that memorable battle was fought. Regent Bridge was officially opened on 18 August 1819 during the visit of Prince Leopold of Saxe Coburg to Edinburgh.

In a letter to Lord melville, Sir John Marjoribanks suggests that they should visit the bridge and while there he would wish "to show its lions" to him. 1819
"Plan - to carry on the line of Princes Street to connect it with The Calton Hilll by a bridge, to erect the new prison, near to Bridewell and to ocntinue the line of road till it joines The Musselburgh Turnpike Road" Estimate ?60,000
"Also desirable to include the unfinished end of York Place in The Act of Parlt... The road through York Place being a great thoroughfare to Leith" 1814

Regent Bridge is a road bridge in Edinburgh where the A1 road enters the New Town from the east and passes over a hollow near Calton Hill.

This bridge carries Waterloo Place over Calton Road to the SW of Calton Hill. Waterloo Place forms the link between Princes Strret (to the W) and Regent Road (to the E).

http://canmore.rcahms.gov.uk/en/site/116897/details/edinburgh+waterloo+place+regent+bridge/

http://www.britishlistedbuildings.co.uk/sc-27945-regent-bridge-carrying-waterloo-place-ove