I have been looking for the original artist of this image also, so I was pleased so see it discussed here. Thanks especially to Keble, who had what I think is the correct answer to a really challenging question. What makes this such a puzzle is that the image originally posted by Velsigne is not its original form, which started out as an 1888 painting by the not-very-well-known German painter George Cornicelius (1825–1898) and entitled "Jesus wird vom Satan versucht" (Christ Tempted by Satan).
If you are interested in learning more about Cornicelius and know German, you can read Karl Siebert's books about him (they are older and in the public domain), and there is also a short bio here:http://de.wikisource.org/wiki/ADB:Cornicelius,_Georg
The painting itself is documented in several books:
Albert Edward Bailey's Art Studies in the Life of Christ
(1917), p. 72 with a reproduction of the painting a few pages later ...http://books.google.com/books?id=_bxAAAAAYAAJ
Also Bailey's The Gospel in Art
One book in particular is Karl Siebert's Georg Cornicelius: Sein Leben Und Seine Werke
I know very little German, so I can't tell you what the book says about the painting, but it does have the image below in the plates at the back of the book. If you look closely, you can see Cornicelius' faint signature in the bottom left hand corner.
From these sources we gather that the painting was done in 1888, that it was 18 x 31 inches, and that in the early 1900s, it was in the collections of the "Konigliche Nationalgalerie zu Berlin," or Berlin National Gallery. I think this corresponds to what is known as the Alte Nationalgalerie in Berlin today. So far, I do not know of any later mention than Bailey's 1917 book. The Nationalgalerie was heavily damaged by bombing in WWII, and it is possible that the original painting was destroyed. Also, when WWII ended, most of the surviving artwork was confiscated and went to different Allied countries while Berlin was being reconstructed. If anybody has any further information about the original, I hope they will share it.
So far, the story of this painting is tragic but not uncommon; here is where it gets a little weird. At some point, another version of this image began circulating, this one without Satan in the background tempting Jesus with a crown and with a halo added to the image. The painter's signature has also been removed. This is the image as posted by Velsigne. If you put the two images side by side, you can see that they are ultimately from the same original.
The unaltered image, if it is not cropped and still bears the signature, is difficult in good conscience to attribute to anybody but Cornicelius. It is the altered image, which has been modified to make it more suitable for devotional purposes, that has been misattributed to various painters. Rembrandt and El Greco have been suggested, but these are easy to dismiss by looking more closely at the styles of those painters. The two false attributions that are the most persistent are Karl Bryullov (1799-1852) and Ivan Kramskoi (1837-1887). There are a number of websites (mostly Russian) that attribute the altered version of this image to either Bryullov or Kramskoi.
I personally like the altered image better for my own purposes, but I cannot help but wonder about the fate of the original painting.
It's "Christ Tempted by Satan" by Georg Cornicelius. It was widely reproduced in Christ and the Fine Arts but I understand the original was destroyed. By my recollection Cornicelius was German.