A theory of the cosmological constant Λ is currently out of reach. Still, one can start from a set of axioms that describe the most desirable properties a cosmological constant should have. This can be seen in certain analogy to the Khinchin axioms in information theory, which fix the most desirable properties an information measure should have and that ultimately lead to the Shannon entropy as the fundamental information measure on which statistical mechanics is based. Here we formulate a set of axioms for the cosmological constant in close analogy to the Khinchin axioms, formally replacing the dependence of the information measure on probabilities of events by a dependence of the cosmological constant on the fundamental constants of nature. Evaluating this set of axioms one finally arrives at a formula for the cosmological constant given by Λ=1ħG(, where G is the gravitational constant, me the electron mass, and α the low-energy limit of the fine structure constant. This formula is in perfect agreement with current WMAP data. Our approach gives physical meaning to the Eddington-Dirac large-number hypothesis and suggests that the observed value of the cosmological constant is not at all unnatural.