Jealousy made him do it.

Literal

Jealousy [subject-が] him [to-に] that [object-を] made-do.

A concise causative sentence. 嫉妬 (しっと, 'jealousy') is the subject and the cause. させた is the past causative of する — literally 'made [him] do.' The structure is [cause]が[person]に[action]をさせた — the standard causative pattern where an emotion or force causes a person to act. The abstraction of jealousy as an active agent is natural in both Japanese and English.