We used two approaches to design proteins with shape and chemical complementarity to the receptor binding domain (RBD) of SARS-CoV-2 Spike protein near the binding site for the human ACE2 receptor. Scaffolds were built around an ACE2 helix that interacts with the RBD, or de novo designed scaffolds were docked against the RBD to identify new binding modes. In both cases, designed sequences were optimized first in silico and then experimentally for target binding, folding and stability. Nine designs bound the RBD with affinities ranging from 100pM to 10nM, and blocked bona fide SARS-CoV-2 infection of Vero E6 cells with IC 50 values ranging from 35 pM to 35 nM; the most potent of these - 56 and 64 residue hyperstable proteins made using the second approach - are roughly six times more potent on a per mass basis (IC 50 ~ 0.23 ng/ml) than the best monoclonal antibodies reported thus far. Cryo-electron microscopy structures of the SARS-CoV-2 spike ectodomain trimer in complex with the two most potent minibinders show that the structures of the designs and their binding interactions with the RBD are nearly identical to the computational models, and that all three RBDs in a single Spike protein can be engaged simultaneously. These hyperstable minibinders provide promising starting points for new SARS-CoV-2 therapeutics, and illustrate the power of computational protein design for rapidly generating potential therapeutic candidates against pandemic threats.