We present the first models of extreme-mass-ratio inspirals within the effective-one-body (EOB) formalism, focusing on quasicircular orbits into nonrotating black holes. We show that the phase difference and (Newtonian-normalized) amplitude difference between analytical EOB and numerical Teukolsky-based gravitational waveforms can be reduced to less than or approximately 10{-1} rad and less than or approximately 2x10{-3}, respectively, after a 2-year evolution. The inclusion of post-Newtonian self-force terms in the EOB approach leads to a phase disagreement of approximately 6-27 rad after a 2-year evolution. Such inclusion could also allow for the EOB modeling of waveforms from intermediate-mass-ratio, quasicircular inspirals.