Farrell was born in 1882 to John Farrell and Margaret Lawson Farrell.[4] His father was a school board officer at the time of his birth and later curator at the Trades House in Glasgow.
Farrell trained as a civil engineer while apprenticed to his brother.[3] As an artist, he was self-taught,[2] and worked in watercolour, as well as making etchings.[3]
He was enlisted into the army as a sapper in June 1916, but was discharged six months later after developing a gastric ulcer.[3]
Following his appointment as a war artist, he went to Flanders, Belgium, in November 1917, and spent three weeks there, painting Highland Light Infantry battalions.[3] The next year he drew the 51st (Highland) Division in France.[3]
He died in 1935 of pneumonia.[4]
An exhibition of his work, the first since 1920,[3] Fred A. Farrell: Glasgow's War Artist, was held at The People's Palace, Glasgow in 2014.