An educator at an elite Melbourne private school who gave students inappropriate descriptions in a document uploaded to the school's intranet has resigned over the saga.

In a letter to families on Thursday, St Michael's Grammar School principal Gerard Houlihan said the school had concluded its investigation into the infamous list and the educator concerned would not be returning.

The racial and physical descriptions, such as "ratty" and "tall goof", appeared next to the names of Year 6 students appearing in a production of The Addams Family, with the list briefly uploaded to the school's intranet .

Other descriptions used for students at the St Kilda-based school, where parents pay up to $40,000 in annual fees, included "eastern European" and "Asian", as well as "anime eyes", "bogan"

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