The embarrassing emails were published in October by New Matilda, an Australian website, and prompted the suspension of Professor Spurr, an Oxford-educated academic and expert on T S Eliot. He claimed the emails were "linguistic play" and were part of a contest with a colleague in which they tried to outdo each other by making incendiary statements.
Professor Spurr, known for his conservative cultural views, contributed to a federal government review of the school curriculum, saying the impact of Aboriginal writers in Australia had been "minimal" and calling for literary studies to place a greater emphasis on "western Judaeo-Christian culture".
The leaked emails emerged only a week after the review was released.
Professor Spurr launched legal action against New Matilda after it published the emails in October, demanding the return of any emails in its possession. The case was settled last week.
The terms of the settlement were confidential but New Matilda is believed to have refused to reveal the source of the emails.
Chris Graham, New Matilda's owner and editor, said he "couldn't give much of a bugger" about Professor Spurr's resignation.
"Can you imagine how a female student, an Asian student, a Muslim student or, God forbid, an Aboriginal student might feel sitting in a lecture theatre listening to Professor Spurr wax lyrical about the power of Judeo-Christian literature?" he wrote on his website.
Professor Spurr was appointed the first ever professor of Australian poetry at Sydney University, the country's oldest university, in 2011.