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We study nonperturbative effects of torus partition function of the TT[over ¯]-deformed 2D conformal field theory (CFT) by resurgence in this Letter and a companion paper. The deformed partition function can be written as an infinite series of the deformation parameter λ. We develop highly efficient methods to compute perturbative coefficients in the λ expansion. To exemplify, the first 600 coefficients for the TT[over ¯]-deformed free boson and free fermion are computed. The method can be generalized to any rational CFTs; we present the key idea in this Letter while relegating details and results to the companion paper. Equipped with the large order perturbative data, we provide convincing numerical evidence that the λ series is asymptotic and not Borel resummable. We extract the nonperturbative contribution by resurgence and propose that they originate from new complex saddle points after analytically continuing the modular parameters in the integral representation of the partition function. The proposal is checked by comparing the predicted asymptotic behavior of the coefficients and large order perturbative data, which match nicely. The implications of these nonperturbative contributions for the Stokes phenomenon, which relates the positive and negative signs of λ, as well as possible comparisons with holography, is also discussed.