Source, in full
Widely attributed but of uncertain provenance. The anecdote of Michelangelo "seeing the angel" is related in Ambition: A Journal of Inspiration to Self Help (January 1916), Volume 11 Issue 1; and in Walter Clemow Lanyon, London Notes and Lectures (1928), p. 13.
Notes from Wikiquote
The anecdote is also described in William Stanyon, Bible Stories & Parables, with a Lesson On, What is Religion? (1884), p. 18 but is only attributed to "a sculptor" and not to Michelangelo specifically.