This paper describes completely the invariant subspaces of the operator of multiplication by a finite Blaschke factor on the Banach space BMOA of analytic functions with bounded mean oscillation on the unit circle in the complex plane. As a simple application, we describe by very elementary means, the invariant subspaces of the co-analytic Toeplitz operator TB on H1. In the simplest case when B(z) = z, the invariant subspaces of TB on H1 were described by fairly deep arguments until the appearance of an elementary proof by two of the authors (Sahni & Singh). In recent times, the common invariant subspaces of the operators of multiplication by B2 and B3, first in the case of z2 and z3, and then for an arbitrary finite Blaschke B, have proved to be critical in the context of Nevanlinna-Pick type interpolation on H2. Thus, keeping in mind the importance of invariant subspaces, we also offer a characterization of the common invariant subspaces of these operators on BMOA. Our proofs are that much more technical. Again, as an application, we obtain the common invariant subspaces of TB2 and TB3 on the Hardy space H1. © 2017, University at Albany. All rights reserved.