The design of modular protein logic for regulating protein function at the posttranscriptional level is a challenge for synthetic biology. Here, we describe the design of two-input AND, OR, NAND, NOR, XNOR, and NOT gates built from de novo-designed proteins. These gates regulate the association of arbitrary protein units ranging from split enzymes to transcriptional machinery in vitro, in yeast and in primary human T cells, where they control the expression of the gene related to T cell exhaustion. Designed binding interaction cooperativity, confirmed by native mass spectrometry, makes the gates largely insensitive to stoichiometric imbalances in the inputs, and the modularity of the approach enables ready extension to three-input OR, AND, and disjunctive normal form gates. The modularity and cooperativity of the control elements, coupled with the ability to de novo design an essentially unlimited number of protein components, should enable the design of sophisticated posttranslational control logic over a wide range of biological functions.