The incident happened in the Quilly Road area of Moneymore on Thursday afternoon and was reported to police shortly after 4pm.
It is understood that the farmer, named as Henry Allen, may have fallen from a wall.
Local Ulster Unionist councillor Robert Kelly paid tribute to the father-of-three, having known the family for many years.
It's a tragedy for his family - our thoughts and prayers are with the whole family.
Robert Kelly, UUP
"Henry has been farming in the area for as long as I know," Mr Kelly told UTV.
"Everybody would tell you that he was a hard-working man and very much family-orientated as well. It's a tragedy."
The Ulster Farmers' Union President Harry Sinclair also spoke of his "deep shock" and "great sadness" following the death.
He said: "I have been speaking with Henry's family who are obviously devastated by his death.
"Henry was a long standing and valued member of the union and he contributed immensely to our work locally and at central level.
"Unfortunately, this very sad accident is another reminder that you can never be too safe on a farm."
The Health and Safety Executive for Northern Ireland confirmed on Friday that it was investigating what had happened.
"HSENI is currently investigating the tragic death of a 70-year-old farmer on a County Londonderry farm," a spokesman said.
"Our deepest sympathies are with the family at this most difficult time."