Blobs, or quasi-spherical emission regions containing relativistic particles and magnetic fields, are often assumed ad hoc in emission models of relativistic astrophysical jets, yet their physical origin is still not well understood. Here, we employ a suite of large-scale 2D particle-in-cell simulations in electron-positron plasmas to demonstrate that relativistic magnetic reconnection can naturally account for the formation of quasi-spherical plasmoids filled with high-energy particles and magnetic fields. Our simulations extend to unprecedentedly long temporal and spatial scales, so we can capture the asymptotic physics independently of the initial setup. We characterize the properties of the plasmoids, continuously generated as a self-consistent by-product of the reconnection process: they are in rough energy equipartition between particles and magnetic fields; the upper energy cutoff of the plasmoid particle spectrum is proportional to the plasmoid width w, corresponding to a Larmor radius ∼0.2 w; the plasmoids grow in size at ∼0.1 of the speed of light, with most of the growth happening while they are still non-relativistic (`first they grow'); their growth is suppressed once they get accelerated to relativistic speeds by the field line tension, up to the Alfvén speed (`then they go'). The largest plasmoids reach a width wmax ∼ 0.2 L independently of the system length L, they have nearly isotropic particle distributions and contain the highest energy particles, whose Larmor radius is ∼0.03 L. The latter can be regarded as the Hillas criterion for relativistic reconnection. We briefly discuss the implications of our results for the high-energy emission from relativistic jets and pulsar winds.