In Drosophila oocytes, dorso-anterior transport of gurken mRNA requires both the Dynein motor and the heterogeneous nuclear ribonucleoprotein (hnRNP) Squid. We show that gurken transcripts are transported directly on microtubules by Dynein in nonmembranous electron-dense transport particles that also contain Squid and the transport cofactors Egalitarian and Bicaudal-D. At its destination, gurken mRNA is statically anchored by Dynein within large electron-dense cytoplasmic structures known as sponge bodies. Egalitarian and Bicaudal-D contribute only to active transport, whereas Dynein and Squid are also required for gurken mRNA anchoring and the integrity of sponge bodies. Disrupting Dynein function disperses gurken mRNA homogeneously throughout the cytoplasm, whereas the loss of Squid function converts the sponge bodies into active transport particles. We propose that Dynein acts as a static structural component for the assembly of gurken mRNA transport and anchoring complexes, and that Squid is required for the dynamic conversion of transport particles to sponge bodies.