Mylne was the grandson of a master stone-mason also called Robert Mylne (1633-1710), remembered particularly for his work as the King's Master Builder at Holyrood Palace in Edinburgh. The grandson was born in Edinburgh and, like many of his contemporaries, travelled to mainland Europe on the 'Grand Tour' to study architecture in Rome and Paris – beating Robert Adam in an architectural competition in 1758.

He returned to Britain in 1759 and almost immediately won a competition to design Blackfriars Bridge over the River Thames in London. The design, with its then novel elliptical arches, excited much interest both in Britain and across Europe; Mylne corresponded with Giovanni Battista Piranesi regarding the project which rivalled the Rialto in Venice.

His other projects included:

• remodelling of Kings Weston (1763)
• Cally House, Kirkcudbright (1763)
• St Cecilia’s Hall, Cowgate, Edinburgh (1765 – the oldest purpose-built concert hall in Scotland)
• Assembly Rooms, King St, St James’s, London (1765)
• various works at Welbeck Abbey, Northumberland (1760s)
• Wormleybury Manor, Hertfordshire (1767-1769)
• The Hunterian Medical School, Great Windmill Street, London (1767 – the building now forms part of the Lyric Theatre)
• Tusmore House, Oxfordshire (1770)
• alterations to Goodnestone House, Kent (1770)
• Addington Palace, south London (1773-1779)
• Bryngwyn House, Powys, Wales (1774)
• The Wick, Richmond-upon-Thames (1775)
• Inverary village and castle, Scotland (1780s)
• Middle Bridge, Romsey, Hampshire (1783)
• Gloucester and Sharpness Canal (1790s)
• Dearne & Dove Canal, South Yorkshire (1793-1804)
• new frontage to Stationers’ Hall, off Fleet Street, London (1800)
• Works at Great Amwell, Hertfordshire, for the New River Company, London (until 1810)