The plasma membrane’s main constituents, i.e., phospholipids and membrane proteins, are known to be organized in lipid-protein functional domains and supercomplexes. No active membrane-intrinsic process is known to establish membrane organization. Thus, the interplay of thermal fluctuations and the biophysical determinants of membrane-mediated protein interactions must be considered to understand membrane protein organization. Here, we used high-speed atomic force microscopy and kinetic and membrane elastic theory to investigate the behavior of a model membrane protein in oligomerization and assembly in controlled lipid environments. We find that membrane hydrophobic mismatch modulates oligomerization and assembly energetics, and 2D organization. Our experimental and theoretical frameworks reveal how membrane organization can emerge from Brownian diffusion and a minimal set of physical properties of the membrane constituents.