  This is the second of a series of articles providing a foundation for the
theory of Drinfeld modular forms of arbitrary rank. In the present part, we
compare the analytic theory with the algebraic one that was begun in a paper of
the third author. For any arithmetic congruence subgroup and any integral
weight we establish an isomorphism between the space of analytic modular forms
with the space of algebraic modular forms defined in terms of the Satake
compactification. From this we deduce the important result that this space is
finite dimensional.
