Born in Shildon, County Durham in 1820, Daniel Adamson was educated at Edward Walton Quaker school. He left school aged 13 to take up an apprenticeship with Timothy Hackworth, engineer to the Stockton and Darlington Railway. After his apprenticeship, he continued to work under Hackworth as a draughtsman and engineer. By 1850, Adamson was the general manager of the Stockton and Darlington engine works. He left the Stockton works in 1850 to become the manager of the Heaton foundry, Stockport.

A year later, Adamson established his own ironworks at Newton Moor, Dukinfield. He expanded the works by building a foundry in 1852, known as the Newton Moor Iron Works. The company manufactured engines and boilers, initially to designs by Hackworth. Adamson's improvements to the boiler designs led to the development of the Manchester Boiler. Expansion of the company through the international success of the Manchester Boiler enabled Adamson to build a new factory in Dukinfield in 1872, under the company name Daniel Adamson & Co. The success of the company also allowed Adamson to experiment with foundry processes and boiler manufacturing, improving boiler design and manufacturing processes. Between 1852 and 1888, Adamson took out nineteen patents relating to engineering and metallurgy.

Adamson's other business interests included the Newton Moor Spinning Company, which he established in 1862, and the Yorkshire Steel and Iron Works set up by Adamson at Penistone, West Riding of Yorkshire, in 1863. The Penistone works were the first in the country to carry out the large-scale manufacture of steel the Bessemer process. Adamson also contributed to the development of the Lincolnshire iron field through the North Lincolnshire Iron Company, which he established at Frodingham in 1864–5. He also held shares in iron works in Cumbria and South Wales.

Adamson is also known for championing the development of the Manchester Ship Canal. In 1882, he arranged a meeting of all interested parties at his home in Didsbury, Manchester, at which the engineering and commercial aspects of creating a shipping waterway between Manchester and Liverpool were discussed. Adamson was elected chairman of the provisional committee to promote the Manchester Ship Canal. The scheme faced opposition from railway companies and the Liverpool port authority, but Adamson successfully pushed it through Parliament. The resulting Act of Parliament in 1885 ensured the canal would be built and allowed the establishment of the Manchester Ship Canal Company. Adamson was appointed first chairman of the board of directors. Lack of funding for the completion of the project led to a reconstitution of the board in 1887, with Adamson resigning as chairman in favour of Lord Egerton of Tatton.

Adamson was active in industry and public life. He was vice-president of the Institution of Mechanical Engineers and president of the Iron and Steel Institute. He was also a member of the Institution of Civil Engineers, the Geological Society, and the British Iron Trades Association. In the public realm, Adamson was a director of the Manchester chamber of commerce, Justice of the Peace for Cheshire and Manchester, and chairman of Dukinfield local board.

Adamson died at home in Didsbury in 1890 and is buried in the Southern Cemetery, Manchester.