Letter #156 is often considered to indicate a direct interference of Eru.
"He was sent by a mere prudent plan of the angelic Valar or
govenors; but Authority had taken up this plan and enlarged it, at
the moment of its failure. `Naked I was sent back- for a brief
time, until my task is done'. Sent back by whom, and whence? Not by
the `gods' whose business is only with this embodied world and its
time; for he passed `out of thought and time'."
However Tolkien refers to it as a "defect in the story" in the same breath (Lett. #156):
"I think the way in which Gandalf's return is presented is a defect,
and one other critic, as much under the spell as yourself, curiously
used the same expression: 'cheating'."
and the passage right after quotation 1) goes (ibid.):
"'I am G. the White, who has returned from death'. 'I am G. the White,
who has returned from death'. Probably he should rather have said to
Wormtongue: 'I have not passed through death (not 'fire and flood') to
bandy crooked words with a serving-man'."
From the drafts presented in HoMe VII we learn that Tolkien hadn't made his mind in this issue by that time:
"Gandalf to reappear again. How did he escape? This might never
be fully explained. He passed through fire - and became the White
and in the earlier versions of "The White Rider" Gandalf doesn't die in Moria and is clothed in white by Galadriel in Lórien. I wonder if Gandalf's death and resurrection was not an afterthought of the Prof....
ToDo: Make this an essay or FAQ