He was born in Ayr and died in Edinburgh. He went into partnership with Thomas Grainger in 1825. The partnership was responsible for many of Scotland's great railway projects. Miller took the lead role in surveying the Edinburgh and Glasgow Railway. He designed many viaducts, including the Lugar Viaduct, Cumnock and the Ballochmyle Viaduct, Mauchline. A plaque commemorating his life was unveiled at Haymarket railway station on the 200th anniversary of his birth. In 2012 a memorial was unveiled at Ayr, funded by the Institution of Civil Engineers. A further plaque to Miller and his work was unveiled in April 2014, at Ballochmyle Viaduct. The plaque was produced by the Institution of Civil Engineers and was jointy unveiled by the ICE President, Geoff French, and East AyrshireProvost, Jim Todd.
Although primarily a railway engineer (including the design of railway stations) he was also responsible for the construction of Granton Harbour.