People have been cheerful since the 15th century and have cheered one another on for just about as long. But you may be surprised, as I was, to learn that we’ve been saying “Cheers!” as “a toast or salutation before drinking,” as the OED puts it, only since the 20th century, and relatively late in the century at that—the OED’s earliest citation is from the Sunday Times of Perth, Australia, September 14, 1930: “The brief toast of ‘Cheers, dears!’” We can also credit the Aussies with Cheers! as a parting salutation (“goodbye”), which they’ve been saying since 1937. The Brits, for their part, took to saying Cheers! to mean thanks by the mid-1970s, if not earlier, according to the OED blog. You can read more about British cheers on Lynne Murphy’s linguistics blog, Separated by a Common Language.
But drinking-salutation cheers as a verb? That was new to me until very recently.