Yahweh is most definitely NOT the correct pronunciation of יהוה. I've made the effort to read the scholarly arguments in favour of "Yahweh" and they turned out to be surprisingly weak. Basicly only the following two things.
First. According to some critical editions of the Stromata of Clement of Alexandria, he claims that יהוה is to be pronounced Ἰαουέ (Yawe). This is to be expected considering that Greek does not have the Hebrew sound 'h', so from Yahweh we get Yawe. Seems convincing, isn't it? Well, no. In the only extant manuscript of the Stromata, the pronunciation of יהוה is given as Ἰαοὺ and not as Ἰαουέ. Then why the critical editions have changed Ἰαοὺ as Ἰαοέυ? Well, because according to their editors Clement had in mind Yahweh. So you see the circular argument here? First, some scholars change Ἰαοὺ as Ἰαοέυ because "we know" יהוה is to be pronounced as Yahweh, then they make the change official in the critical edition of the Stromata, and finaly other scholars use this as the primary argument in support of Yahweh.
Second. There is some evidence that Samaritans pronounced יהוה as Yave. Linguistically the omission of 'h' and the replacement of 'w' by 'v' is possible. Does this imply that Jewish pronunciation of יהוה was Yahweh? It is up to you to decide.
My personal hypothesis is that Yave is simply a translation of יהוה in Aramaic. Morphologically יהוה means "He is" (not "I am"). The letter י is "He" and the root הוה is the verb "to be". Now let us translate this to Aramaic. י is also י and הוה is הוי, so in result we obtain יהוי. One millennium before Christ the pronunciation of this form must have been 'Yahuwiy' but then it evolved many times: Yahuwiy > Yahuwe > Yahwe > Yahve > Yave.
Is it possible to give a similar linguistic explanation of Yahweh as pronunciation of יהוה? Many have tried but their arguments are not convincing.
So יהוה is not Yahweh, nor it is Jehowah. As for the actual pronunciation of יהוה we have many evidences in Greek documents, one (by Jerome) in Latin and we also have some Jewish teophoric names in Assyrian cuneiform texts. All these evidences agree with one another but, nonetheless, they are ignored.