Engineered living materials (ELMs) embed living cells in a biopolymer matrix to create materials with tailored functions. While bottom-up assembly of macroscopic ELMs with a de novo matrix would offer the greatest control over material properties, we lack the ability to genetically encode a protein matrix that leads to collective self-organization. Here we report growth of ELMs from Caulobacter crescentus cells that display and secrete a self-interacting protein. This protein formed a de novo matrix and assembled cells into centimeter-scale ELMs. Discovery of design and assembly principles allowed us to tune the composition, mechanical properties, and catalytic function of these ELMs. This work provides genetic tools, design and assembly rules, and a platform for growing ELMs with control over both matrix and cellular structure and function.