  We present the DESI 2024 galaxy and quasar baryon acoustic oscillations (BAO)
measurements using over 5.7 million unique galaxy and quasar redshifts in the
range 0.1<z<2.1. Divided by tracer type, we utilize 300,017 galaxies from the
magnitude-limited Bright Galaxy Survey with 0.1<z<0.4, 2,138,600 Luminous Red
Galaxies with 0.4<z<1.1, 2,432,022 Emission Line Galaxies with 0.8<z<1.6, and
856,652 quasars with 0.8<z<2.1, over a ~7,500 square degree footprint. The
analysis was blinded at the catalog-level to avoid confirmation bias. All
fiducial choices of the BAO fitting and reconstruction methodology, as well as
the size of the systematic errors, were determined on the basis of the tests
with mock catalogs and the blinded data catalogs. We present several
improvements to the BAO analysis pipeline, including enhancing the BAO fitting
and reconstruction methods in a more physically-motivated direction, and also
present results using combinations of tracers. We present a re-analysis of SDSS
BOSS and eBOSS results applying the improved DESI methodology and find scatter
consistent with the level of the quoted SDSS theoretical systematic
uncertainties. With the total effective survey volume of ~ 18 Gpc$^3$, the
combined precision of the BAO measurements across the six different redshift
bins is ~0.52%, marking a 1.2-fold improvement over the previous
state-of-the-art results using only first-year data. We detect the BAO in all
of these six redshift bins. The highest significance of BAO detection is
$9.1\sigma$ at the effective redshift of 0.93, with a constraint of 0.86%
placed on the BAO scale. We find our measurements are systematically larger
than the prediction of Planck-2018 LCDM model at z<0.8. We translate the
results into transverse comoving distance and radial Hubble distance
measurements, which are used to constrain cosmological models in our companion
paper [abridged].
