Matrix stiffness potently regulates cellular behaviour in various biological contexts. In breast tumours, the presence of dense clusters of collagen fibrils indicates increased matrix stiffness and correlates with poor survival. It is unclear how mechanical inputs are transduced into transcriptional outputs to drive tumour progression. Here we report that TWIST1 is an essential mechanomediator that promotes epithelial-mesenchymal transition (EMT) in response to increasing matrix stiffness. High matrix stiffness promotes nuclear translocation of TWIST1 by releasing TWIST1 from its cytoplasmic binding partner G3BP2. Loss of G3BP2 leads to constitutive TWIST1 nuclear localization and synergizes with increasing matrix stiffness to induce EMT and promote tumour invasion and metastasis. In human breast tumours, collagen fibre alignment, a marker of increasing matrix stiffness, and reduced expression of G3BP2 together predict poor survival. Our findings reveal a TWIST1-G3BP2 mechanotransduction pathway that responds to biomechanical signals from the tumour microenvironment to drive EMT, invasion and metastasis.