When the Cathedral bell tolled just after dark, the Mexican population of Santa Fe fell upon their knees, and all American Catholics as well. Many others who did not kneel prayed in their hearts. Eusabio and the Tesuque boys went quietly away to tell their people; and the next morning the old Archbishop lay before the high altar in the church he had built. (9.8.6)
At the end of this book, Willa Cather lives up to her title's promise. Death actually comes for the Archbishop and Father Latour dies in his old age. He has lived a long and significant life in New Mexico, and as a sign of respect, people come from all over Santa Fe to honor his memory in the very Cathedral that Latour had built.
Latour has spent the entire second half of this book thinking about his own mortality, and when the time of death arrives, he feels confident that he made the right decisions and lived a good life. And there's not much more you can ask for in your final moments. This is a happy ending, but also a super realistic one.