Seward was born in Lancaster. His first education was at Lancaster Grammar School and he then went on to St John's College, Cambridge, intending to fulfil parents' wish that he would dedicate his life to the Church. His boyhood interest in botany and zoology soon resurfaced, helped along by inspiring lectures from William Crawford Williamson. His aptitude soon became apparent and he was appointed lecturer in botany at Cambridge University in 1890, later becoming a tutor at Emmanuel, and still later succeeding Harry Marshall Ward as Professor of Botany, Cambridge University from 1906 to 1936. He was joint editor (with Francis Darwin) of More letters of Charles Darwin (1903). He was elected as fellow of the Royal Society in 1898 and was awarded the Murchison Medal of the Geological Society of London in 1908. In 1931 Seward dismissed the notion of a biological origin of stromatolites. This rejection became known as "Seward's folly".
Seward's studies of Mesozoic palaeobotany earned him membership of the Royal Society at the youthful age of thirty-five. He devoted a great deal of time to education, both as college and departmental administrator, and as writer on educational matters. This botanist is denoted by the author abbreviation Seward when citing a botanical name.
Seward died in Oxford, aged 77.