The Dark Energy Survey (DES) Collaboration presents cosmological results from a combined analysis of galaxy clustering and weak gravitational lensing using 1321 deg² of $griz$ imaging data from the first year of the DES. The analysis combines three two-point functions: cosmic shear correlation, galaxy angular autocorrelation, and galaxy-shear cross-correlation. The robustness of these results is demonstrated through independent pairs of galaxy shape, photometric redshift estimation, and likelihood analysis pipelines. The data are modeled in flat $\Lambda$CDM and $w$CDM cosmologies, marginalizing over 20 nuisance parameters. The DES Y1 constraints on cosmological parameters are consistent with those from Planck cosmic microwave background measurements, allowing for a comparison of structure in the early and late Universe. The DES Y1 best-fit values for $S_8$ and $\Omega_m$ are lower than Planck's central values but are consistent with Planck data in the context of $\Lambda$CDM. Combining DES Y1 with external data sets, the tightest constraints on cosmological parameters are derived, providing a powerful test of the $\Lambda$CDM model and its extensions.The Dark Energy Survey (DES) Collaboration presents cosmological results from a combined analysis of galaxy clustering and weak gravitational lensing using 1321 deg² of $griz$ imaging data from the first year of the DES. The analysis combines three two-point functions: cosmic shear correlation, galaxy angular autocorrelation, and galaxy-shear cross-correlation. The robustness of these results is demonstrated through independent pairs of galaxy shape, photometric redshift estimation, and likelihood analysis pipelines. The data are modeled in flat $\Lambda$CDM and $w$CDM cosmologies, marginalizing over 20 nuisance parameters. The DES Y1 constraints on cosmological parameters are consistent with those from Planck cosmic microwave background measurements, allowing for a comparison of structure in the early and late Universe. The DES Y1 best-fit values for $S_8$ and $\Omega_m$ are lower than Planck's central values but are consistent with Planck data in the context of $\Lambda$CDM. Combining DES Y1 with external data sets, the tightest constraints on cosmological parameters are derived, providing a powerful test of the $\Lambda$CDM model and its extensions.