While there has been progress in the de novo design of small globular miniproteins (50-65 residues) to bind to primarily concave regions of a target protein surface, computational design of minibinders to convex binding sites remains an outstanding challenge due to low level of overall shape complementarity. Here, we describe a general approach to generate computationally designed proteins which bind to convex target sites that employ geometrically matching concave scaffolds. We used this approach to design proteins binding to TGFβRII, CTLA-4 and PD-L1 which following experimental optimization have low nanomolar to picomolar affinities and potent biological activity. Co-crystal structures of the TGFβRII and CTLA-4 binders in complex with the receptors are in close agreement with the design models. Our approach provides a general route to generating very high affinity binders to convex protein target sites.