To deal with complex optimization problems plagued with computationally expensive fitness functions, the use of surrogates to replace the original functions within the evolutionary framework is becoming a common practice. However, the appropriate datacentric approximation methodology to use for the construction of surrogate model would depend largely on the nature of the problem of interest, which varies from fitness landscape and state of the evolutionary search, to the characteristics of search algorithm used. This has given rise to the plethora of surrogate-assisted evolutionary frameworks proposed in the literature with ad hoc approximation/surrogate modeling methodologies considered. Since prior knowledge on the suitability of the data centric approximation methodology to use in surrogate-assisted evolutionary optimization is typically unavailable beforehand, this paper presents a novel evolutionary framework with the evolvability learning of surrogates (EvoLS) operating on multiple diverse approximation methodologies in the search. Further, in contrast to the common use of fitness prediction error as a criterion for the selection of surrogates, the concept of evolvability to indicate the productivity or suitability of an approximation methodology that brings about fitness improvement in the evolutionary search is introduced as the basis for adaptation. The backbone of the proposed EvoLS is a statistical learning scheme to determine the evolvability of each approximation methodology while the search progresses online. For each individual solution, the most productive approximation methodology is inferred, that is, the method with highest evolvability measure. Fitness improving surrogates are subsequently constructed for use within a trust-region enabled local search strategy, leading to the self-configuration of a surrogate-assisted memetic algorithm for solving computationally expensive problems. A numerical study of EvoLS on commonly used benchmark problems and a real-world computationally expensive aerodynamic car rear design problem highlights the efficacy of the proposed EvoLS in attaining reliable, high quality, and efficient performance under a limited computational budget.