The road under this viaduct was the track bed of the Penydarren and Merthyr tramroad on which Richard Trevithick an the first ever steam locomotive between the Penydarren Iron Works in Merthyr Tydfil to the wharf of the Glamorgan Canal at modern day Abercynon. Ten tons of iron in five wagons with 70 people sitting on top did the journey on 21 February 1804. The opening of the Taff Vale Railway signed the death warrant of Trevithick's tramroad and it closed in 1851.

There are two separate phases of build to the Quakers Yard Viaduct crossing the River Taff with the first being under the control of Isambard Kingdom Brunel for the Taff Vale Railway which connected Merthyr Tydfil to Cardiff Docks. The viaduct was a single track and the first train used it on 21 April 1841.

In 1861-62 the second viaduct was added when the busy Taff Vale Railway was widened to accommodate a double track. In 1988 the structure was given a Grade II listing.