This is an ancient catholic prophecy first penned by RCC Bishop Malachy of Armagh, Irland in the 12th century. After experiencing the vision that was the source of this prophecy, Malachy gave a written copy of his vision to Pope Innocent II. But it never saw the light of day, likely being read by the then pope and subsequently filed away in the Roman Archives until its rediscovery by Benedictine monk Arnold Wion in approximately 1590 where it was taken out, read, and then distributed.
There is considerable debate about the accuracy of the prophecy, as some argue that it is a fake due to several circumstances, including the fact that the accuracy of the popes described in the prophecy up to 1595 are spot on accurate, but after that time the accuracy goes down considerably. However, others argue that it has maintained its accuracy throughout the centuries. As this prophecy is of Roman Catholic origins, one is advised to be circumspect when reading and studying it as the truth of whether this is a real prophecy or its fulfillment will actually happen is in question.
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The Prophecy of St. Malachy
What is the prophecy of St. Malachy? (GotQuestions.org) - Report Link
Prophecy: 
Vision: 
Dream: 