Molecular motors actively transport many types of cargo along the cytoskeleton in a wide range of organisms. One class of cargo is localized mRNAs, which are transported by myosin on actin filaments or by kinesin and dynein on microtubules. How the cargo is kept at its final intracellular destination and whether the motors are recycled after completion of transport are poorly understood. Here, we use a new RNA anchoring assay in living Drosophila blastoderm embryos to show that apical anchoring of mRNA after completion of dynein transport does not depend on actin or on continuous active transport by the motor. Instead, apical anchoring of RNA requires microtubules and involves dynein as a static anchor that remains with the cargo at its final destination. We propose a general principle that could also apply to other dynein cargo and to some other molecular motors, whereby cargo transport and anchoring reside in the same molecule.