You can sort of see when the switch happened with Google’s NGRAM viewer, which has the digitized texts of millions of books dating back to 1500 AD. As you can see, both spellings were common until the late 1800’s, after which “Hindu” picks up steam while “Hindoo” fades into obscurity.

A lot of words have varied spellings in the early times when spelling wasn’t standardized as much as it is today, so it’s not unexpected. In fact, for an English speaker, “Hindoo” is more phonetically correct than “Hindu”. These changes were driven by Europeans, since Indians were not writing books in English at the time.

I have a theory about why this change occurred, which is that it was due to the appearance of the word “Hinduism”. As you probably know, this is a European word, unfamiliar to Indians in the past. In India, the original term for the religion is “Sanatana Dharma” (the eternal dharma or order), which goes back to the Rig Veda, around 1,800 BC. Most Hindus in the past typically referred to themselves by sect, for example, Vaishnavs or Shaivs, or whatever. But the uniting principle behind all these sects were the Vedas, which were common to all, so scholarly mentions of the native religion of India by Indians would have referred to it as “Sanatana Dharma”.

“Hind” is the Persian word for the river Indus, and the Persians referred to Indians as “Hindi”, meaning people living beyond the Indus, or “Hindoo” as the singular, meaning “a person from across the Indus”. The Europeans already had words for both: “India” and “Indian” going back to ancient Greek times, but when they arrived in India they adopted the Persian usage, because Persian was the language of the Mughal Court, with which they dealt.

Originally, the word “Hindu” or “Hindoo” was not associated with the religion, it simply meant anyone from the region of India. But eventually, Europeans invented the word “Hinduism” to refer to the particular dharmic religions of India that Indians refer to as “Sanatana Dharma”. As I said above, the first use of this word appears in 1865 in the NGRAM viewer, though I would not rely too heavily on that. After all, it only represents a sample of books, not everything that’s been written. It’s possible that “Hinduism” was used by Europeans earlier than 1865, but its usage was common enough by 1865 to show up in the NGRAM viewer.

So my theory is that both “Hindu” and “Hindoo” were accepted alternate spellings in Europe since the Europeans arrived in the subcontinent, but around the mid 19th century, the appearance of the word “Hinduism” in print made people favor the “Hindu” spelling more, and the other became obsolete.

There is also a negative association with “Hindoo” in modern times, where it was often used as a slur back in the 50’s and 60’s in the UK and US. Perhaps a deliberate choice of the archaic spelling evoked notions of primitiveness, which was the intended effect of the slur. We do see a sharp decline of the “Hindoo” spelling around that period, after which it pretty much vanishes from printed texts. Perhaps this was an effect of its derogatory use, as people started avoiding it in print. But the predominance of “Hindu” over “Hindoo” goes back much earlier, to the mid 19th century, and this, I think, may be related to the appearance of the word “Hinduism”.