  We establish a noncommutative generalisation of the Borel-Weil theorem for
the Heckenberger-Kolb calculi of the quantum Grassmannians. The result is
formulated in the framework of quantum principal bundles and noncommutative
complex structures, and generalises previous work of a number of authors on
quantum projective space. As a direct consequence we get a novel noncommutative
differential geometric presentation of the twisted Grassmannian coordinate ring
studied in noncommutative projective geometry. A number of applications to the
noncommutative K\"ahler geometry of the quantum Grassmannians are also given.
