The artist will, without any doubt whatsoever, enthusiastically endorse your using the picture on a book cover. It's just the way artists roll.
Cultural note: My criteria, if and when asked for art--Do NOT place any print or anything else over the image. And if you use a detail rather than the full image, you must, in the credit, specify "detail". Also, be sure to use a high resolution image of the work, otherwise it will pixilate. It all sounds obvious, except for maybe the first point. I think most artists are averse to copy running over their work.
Excellent idea to use original art that you own on a book cover!