We present the first cosmology results from large-scale structure in the Dark Energy Survey (DES) spanning 5000 deg$^2$. We perform an analysis combining three two-point correlation functions (3$times$2pt): (i) cosmic shear using 100 million source galaxies, (ii) galaxy clustering, and (iii) the cross-correlation of source galaxy shear with lens galaxy positions. The analysis was designed to mitigate confirmation or observer bias; we describe specific changes made to the lens galaxy sample following unblinding of the results. We model the data within the flat $Lambda$CDM and $w$CDM cosmological models. We find consistent cosmological results between the three two-point correlation functions; their combination yields clustering amplitude $S_8=0.776^{+0.017}_{-0.017}$ and matter density $Omega_{mathrm{m}} = 0.339^{+0.032}_{-0.031}$ in $Lambda$CDM, mean with 68% confidence limits; $S_8=0.775^{+0.026}_{-0.024}$, $Omega_{mathrm{m}} = 0.352^{+0.035}_{-0.041}$, and dark energy equation-of-state parameter $w=-0.98^{+0.32}_{-0.20}$ in $w$CDM. This combination of DES data is consistent with the prediction of the model favored by the Planck 2018 cosmic microwave background (CMB) primary anisotropy data, which is quantified with a probability-to-exceed $p=0.13$ to $0.48$. When combining DES 3$times$2pt data with available baryon acoustic oscillation, redshift-space distortion, and type Ia supernovae data, we find $p=0.34$. Combining all of these data sets with Planck CMB lensing yields joint parameter constraints of $S_8 = 0.812^{+0.008}_{-0.008}$, $Omega_{mathrm{m}} = 0.306^{+0.004}_{-0.005}$, $h=0.680^{+0.004}_{-0.003}$, and $sum m_{ u}<0.13 ;mathrm{eV; (95% ;CL)}$ in $Lambda$CDM; $S_8 = 0.812^{+0.008}_{-0.008}$, $Omega_{mathrm{m}} = 0.302^{+0.006}_{-0.006}$, $h=0.687^{+0.006}_{-0.007}$, and $w=-1.031^{+0.030}_{-0.027}$ in $w$CDM. (abridged)
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