When and why did the USA change the spelling of the word 'colour' to 'color'?

Because "color" is the American spelling, and "colour" is the British spelling.

https://en.wikipedia.org/wiki/Spelling_differences

American spellings, such as center, color, and traveler, were introduced, although often not created, by Noah Webster (An American Dictionary of the English Language, 1828), who was a strong proponent of spelling reform for a variety of reasons, both philological and nationalistic.

https://en.wikipedia.org/wiki/Spelling_differences

Actually, the spelling of "colour" was derived from early Anglo-French (that is, Norman). The original Latin was "color."

So says the etymology for the word in the online OED.

Over the past 400 years, the form of the language used in the Americas – especially in the United States – and that used in the United Kingdom and the rest of the British Isles have diverged in many ways, leading to the dialects now commonly referred to as American English and British English. Differences between the two include pronunciation, grammar, vocabulary (lexis), spelling, punctuation, idioms, formatting of dates and numbers, and so on. A small number of words have completely different meanings between the two dialects or are even unknown or not used in one of the dialects. One particular contribution towards formalizing these differences came from Noah Webster, who wrote the first American dictionary (published 1828) with the intention of showing that people in the United States spoke a different dialect from Britain.

https://en.wikipedia.org/wiki/American_and_British_English_differences

It seems likely that it was the British who changed the spelling from color to colour, rather than the reverse.
In 19th century census returns for example it is very common to find an occupation as "laborer" rather than labourer as we would write it today.

Color or Colour: Most words of this category derive from Latin non-agent nouns having nominative -or; the first such borrowings into English were from early Old French and the ending was -or or -ur. After the Norman Conquest, the termination became -our in Anglo-French in an attempt to represent the Old French pronunciation of words ending in -or.

Webster's 1828 dictionary featured only -or and is generally given much of the credit for the adoption of this form in the US. By contrast, Dr Johnson's 1755 dictionary used the -our spelling for all words still so spelled in Britain, as well as for emperour, errour, governour, horrour, tenour, terrour, and tremour, where the u has since been dropped. Johnson, unlike Webster, was not an advocate of spelling reform and for the most part simply recorded what he found. (Same link as above).

https://en.wikipedia.org/wiki/British_spelling