One of the most infamous examples is syphilis, which is believed to have arrived in Europe on some of the first voyages to the Americas. It was first identified in 1495 but did not receive an official name until much later.
Some have theorized that syphillis was present but unrecognized in Europe before Columbus, but the evidence on that was analyzed in a 2011 paper and found to be inconclusive. There may yet be remains in Africa or other portions of the "Old World" that offer evidence of pre-Columbian syphilis, but if so, they haven't been found yet.
If you'll permit me to think outside the box, I'll also offer Phytophthora infestans, the cause of potato blight and the Irish potato famine. Similarly, a few decades later, the Phylloxera aphid ravaged French and European vineyards starting in the late 1850s and early 1860s. That disease was only stopped when European vines were grafted to American rootstock resistant to the aphid (resistant because Phylloxera was endemic in the Americas).