The nucleation and growth of clathrate hydrates of a hydrophobic guest comparable to methane or carbon dioxide are studied by molecular dynamics simulations of two-phase systems. The crystallization proceeds in two steps: First, the guest molecules concentrate in "blobs", amorphous clusters involving multiple guest molecules in water-mediated configurations. These blobs are in dynamic equilibrium with the dilute solution and give birth to the clathrate cages that eventually transform it into an amorphous clathrate nucleus. In a second step, the amorphous clathrate transforms into crystalline clathrate. At low temperatures, the system can be arrested in the metastable amorphous clathrate phase for times sufficiently long for it to appear as an intermediate in the crystallization of clathrates. The "blob mechanism" unveiled in this work synthesizes elements of the labile cluster and local structuring hypotheses of clathrate nucleation and bears strong analogies to the two-step mechanisms of crystallization of proteins and colloids.