Global cellular responses induced by epidermal growth factor (EGF) receptor (EGFR) occur immediately with a less than 1% occupancy among tens of thousands of EGFR molecules on single cell surface. Activation of EGFR requires the formation of a signaling dimer of EGFR bound with a single ligand to each molecule. How sufficient numbers of signaling dimers are formed at such low occupancy rate is still not known. Here, we have analyzed the kinetics of EGF binding and the formation of the signaling dimer using single-molecule imaging and mathematical modeling. A small number of EGFR on the cell surface formed dimeric binding sites, which bound EGF two orders of magnitude faster than the monomeric binding sites. There was a positive cooperative binding of EGF to the dimeric binding sites through a newly discovered kinetic intermediate. These two mechanisms facilitate the formation of signaling dimers of EGF/EGFR complexes.