Aberrant regulation of RNA stability has an important role in many disease states. Deregulated post-transcriptional modulation, such as that governed by microRNAs targeting linear sequence elements in messenger RNAs, has been implicated in the progression of many cancer types. A defining feature of RNA is its ability to fold into structures. However, the roles of structural mRNA elements in cancer progression remain unexplored. Here we performed an unbiased search for post-transcriptional modulators of mRNA stability in breast cancer by conducting whole-genome transcript stability measurements in poorly and highly metastatic isogenic human breast cancer lines. Using a computational framework that searches RNA sequence and structure space, we discovered a family of GC-rich structural cis-regulatory RNA elements, termed sRSEs for structural RNA stability elements, which are significantly overrepresented in transcripts displaying reduced stability in highly metastatic cells. By integrating computational and biochemical approaches, we identified TARBP2, a double-stranded RNA-binding protein implicated in microRNA processing, as the trans factor that binds the sRSE family and similar structural elements--collectively termed TARBP2-binding structural elements (TBSEs)--in transcripts. TARBP2 is overexpressed in metastatic cells and metastatic human breast tumours and destabilizes transcripts containing TBSEs. Endogenous TARBP2 promotes metastatic cell invasion and colonization by destabilizing amyloid precursor protein (APP) and ZNF395 transcripts, two genes previously associated with Alzheimer's and Huntington's disease, respectively. We reveal these genes to be novel metastasis suppressor genes in breast cancer. The cleavage product of APP, extracellular amyloid-α peptide, directly suppresses invasion while ZNF395 transcriptionally represses a pro-metastatic gene expression program. The expression levels of TARBP2, APP and ZNF395 in human breast carcinomas support their experimentally uncovered roles in metastasis. Our findings establish a non-canonical and direct role for TARBP2 in mammalian gene expression regulation and reveal that regulated RNA destabilization through protein-mediated binding of mRNA structural elements can govern cancer progression.