Born in Conway, New Hampshire, Farrington was the son of Jeremiah and Molly (Swan) Farrington. He attended the common schools in Conway and graduated from Fryeburg Academy in 1814.
Farrington's early life was marked by his birth in Conway, New Hampshire, to parents Jeremiah and Molly (Swan) Farrington. His education began at the common schools in his hometown of Conway before he went on to graduate from Fryeburg Academy in 1814.