Born in Paisley, Johnston rose from modest beginnings to become 'one who has done more than has ever yet been done to preach science to the masses'. After study at Glasgow University, Johnston moved to Durham in 1826 and established a private school in Claypath. After visits to the famous scientists Berzelius and Orsted, Johnston helped to form the British Association and was responsible for the record of its first meeting in York in 1831.
He was appointed lecturer in Chemistry and Mineralogy at the newly-founded University of Durham in 1833 and remained there until his death in 1855. His great claim to fame lies in his popularisation of science; his Catechism of Agricultural Chemistry and Geology (1844) went through 37 editions in his lifetime and was translated into many languages. His last work The Chemistry of Common Life (2 volumes, 1856) was a success and was continued by George Henry Lewes in 1859, and Professor A. H. Church in 1879.
Johnston was also an educational benefactor and his will enabled the Johnston Laboratory to be created in the Durham College of Science in Newcastle. Little more had been done by 1890, however, when a complaint led to the establishment of a co-educational school in South Street. This school, now located in the west of the city, has a high reputation as a comprehensive.