In American English, spelt primarily refers to the hardy wheat grown mostly in Europe, and the verb spell makes spelled in the past tense and as a past participle. In all other main varieties of English, spelt and spelled both work as the past tense and past participle of spell, at least where spell means to form words letter by letter or (with out) to make clear. Outside the U.S., the two forms are interchangeable in these uses, and both are common.
But when spell carries the sense to temporarily relieve (someone) from work, spelled is the preferred form throughout the English-speaking world. This is a minor point, though, as this sense of spell is rarely used outside the U.S., where it is most common.
Spelled is not a recent Americanism, as many people assume (including some who have commented on this post). Both spelled and spelt are old, and examples of each are easily found in historical Google Books searches covering the 17th and 18th centuries. It is true, however, that spelt was ascendant everywhere through most of the 19th century. This ended when Americans permanently settled on spelled around 1900.
American publications (and Canadian ones to a lesser extent) prefer spelled over spelt for all uses relating to the verb spell—for example:
They spelled out broad, clear theories of human behavior. [San Francisco Chronicle]
While the comment carried an obvious implication, he spelled it out for the first time Tuesday. [Globe and Mail (link now dead)]
Trump’s advisers later note that “absolutely” and “lime” are spelled wrong. [Star-Ledger]
Unless we’re missing something, U.K., Irish, Australian, and New Zealand writers make no distinction between spelled and spelt. Don’t bother trying to find any difference between the words in these examples, which we have chosen more or less at random, because there is none:
Will they skip through thousands of mundane and badly spelled missives from authors? [Independent]
Her name was Joanna (or “Jo”) Hiffernan – you probably want to correct that, but it was how both she and her father spelt it. [Irish Times]
The sect’s strict rules are clearly spelled out on the wall of the gates. [New Zealand Herald]
He has also calmly spelt out his own desire to end his life when he chooses, not when the disease does. [Daily Mail]
Campaigners behind a community bid to rescue Leith Waterworld today spelled out how the leisure pool could be given a new lease of life. [Scotsman]
Their temperamental differences are spelt out in other ways. [Sydney Morning Herald]
The following ngram shows the use of spelt and spelled in American books published in the 20th century. It shows that spelt has barely registered against spelled during this time: