"execution by electricity," 1889, American English; noun of action from electrocute. Meaning "any death by electricity" is from 1897.
Electrocution, unless better performed than in the first instance, is a retrograde step rather than the contrary. The preliminary arrangements: the shaving of the head, the cutting of the clothing, the strapping in a chair, add much to the horror of the occasion. It is safe to say that electrocution is not the coming method of execution. [The Medical Era, vol. vii, no. 9, Sept. 1890]