Blessed is the past tense and past participle of bless. Blest is an archaic form that shows up mainly in references to old, mostly poetical texts and as a poetic affectation. Elsewhere, it has been pushed out of the language. This is the case throughout the English-speaking world.
Both spellings descend from older forms in Old and Middle English, and both developed around the 14th century,1 though blessed is probably a little older. Blessed is one of a number of -ed words that gained a -t variant when the vowel sound in -ed was dropped around the 16th century.2 Blest was never more common than blessed, though, and today we remember it mainly because it appears in some great literary works of the early modern era. Shakespeare, for example, used it a few dozen times (at least in the early renderings of his plays, which were assembled by several people with different spelling preferences, and where blessed is actually about twice as common as blest). It is probably significant that in our searches for historical examples of the two forms, most instances of blest are in poetry. Blessed, meanwhile, is disproportionately common in Christian texts.
The old, two-syllable pronunciation of blessed (bless-id) survives in religious oratory and in some religious phrases, but elsewhere the word’s ending is pronounced like that of other words ending in -essed—that is, est instead of ess-id.
Rude am I in my speech, / And little blest with the soft phrase of peace. [Othello, Shakespeare (1604)]
Thrice all hail! and blessed be / Those that love and honor thee. ["Phil'arete," George Wither (early 17th century)]
Blest paper-credit! last and best supply! / That lends corruption lighter wings to fly! [The Dunciad, Alexander Pope (1729)]
Though blessed with only a trembling faith herself, she was desirous of animating the confidence or others. [The Evangelical Magazine, vol. 10 (1802)]
Having few wants, blest with a climate in which the rudest methods of cultivation produce abundance of food for their use, they out to be a happy and contented race. [Popular Science (1889)]
Hurriedly Bilbo stepped back and blessed the luck of his ring. [The Hobbit, J.R.R. Tolien (1937)]
How blest we are to be able to rely on lawfully constituted government backed by such documents as our Constitution and the Bill of Rights. [Gainesville Sun (1991)]
He has always been blessed with the sort of temperament that enables him to ignore all distractions. [Telegraph (2012)]