Long story short, the correct form is inhabited. The reason why people (especially non-native speakers) tend to think that the word is “inhabitated” is that there are quite a few polysyllabic verbs that end with “tate”, e.g. agitate, hesitate, levitate, and not so many that end just with a “t”.
However, there is no such verb as “inhabitate” in modern English. Some dictionaries list “inhabitate” as an archaic version of “inhabit”, but even that does not seem to be supported by actual data. “Inhabitate” has not been used in English literature since at least the 15th century (which is as far as my sources go), apart from a tiny number of cases that can be considered spelling errors.
The only form that existed alongside “inhabit” in the past is “inhabite”, which was somewhat widespread around the year 1600, but such spelling is now considered completely obsolete.