We study selective upconversion of optical signals according to their detailed transverse electromagnetic modes and demonstrate its proof of operation in a nonlinear crystal. The mode selectivity is achieved by preparing the pump wave in an optimized spatial profile to drive the upconversion. For signals in the Laguerre-Gaussian modes, we show that a mode can be converted with up to 60 times higher efficiency than an overlapping, but orthogonal, mode. This nonlinear optical approach may find applications in compressive imaging, pattern recognition, quantum communications, and others, where the existing linear optical methods are limited.