Forsyth was born at Old Meldrum, in Aberdeenshire, and trained as a gardener at the Chelsea Physic Garden. In 1779 he was appointed as chief superintendent of the royal gardens at Kensington and St James’s.
His great grandson was the gardener and landscape architect Joseph Forsyth Johnson (1840-1906). He in turn was the great grandfather of the British entertainer Bruce Forsyth.