Splashback refers to the process of matter that is accreting onto a dark matter halo reaching its first orbital apocenter and turning around in its orbit. The clustercentric radius at which this process occurs, r_(sp), defines a halo boundary that is connected to the dynamics of the cluster. A rapid decline in the halo profile is expected near r_(sp). We measure the galaxy number density and weak lensing mass profiles around REDMAPPER galaxy clusters in the first-year Dark Energy Survey (DES) data. For a cluster sample with mean M_(200m) mass ≈2.5 × 10^(14) M⊙, we find strong evidence of a splashback-like steepening of the galaxy density profile and measure r_(sp) = 1.13 ± 0.07 h^(−1) Mpc, consistent with the earlier Sloan Digital Sky Survey measurements of More et al. and Baxter et al. Moreover, our weak lensing measurement demonstrates for the first time the existence of a splashback-like steepening of the matter profile of galaxy clusters. We measure r_(sp) = 1.34 ± 0.21 h^(−1) Mpc from the weak lensing data, in good agreement with our galaxy density measurements. For different cluster and galaxy samples, we find that, consistent with ΛCDM simulations, r_(sp) scales with R_(200m) and does not evolve with redshift over the redshift range of 0.3–0.6. We also find that potential systematic effects associated with the REDMAPPER algorithm may impact the location of r_(sp). We discuss the progress needed to understand the systematic uncertainties and fully exploit forthcoming data from DES and future surveys, emphasizing the importance of more realistic mock catalogs and independent cluster samples