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New apatite and zircon fission track and (U‐Th)/He analyses serve to document the bedrock cooling history of the central Nepalese Himalaya near the Annapurna Range. We have obtained 82 apatite fission track (AFT), 7 zircon fission track (ZFT), and 7 apatite (U‐Th)/He (AHe) ages from samples collected along the Marsyandi drainage, including eight vertical relief profiles from ridges on either side of the river averaging more than 2 km in elevation range. In addition, three profiles were sampled along ridge crests that also lie ∼2 km above the adjacent valleys, and a transect of >20 valley bottom samples spans from the Lesser Himalaya across the Greater Himalaya and into the Tethyan strata. As a consequence, these data provide one of the more comprehensive low‐temperature thermochronologic studies within the Himalaya. Conversely, the youthfulness of this orogen is pushing the limits of these dating techniques. AFT ages range from >3.8 to 0 Ma, ZFT ages from 1.9 to 0.8 Ma, and AHe ages from 0.9 to 0.3 Ma. Most ridges have maximum ages of 1.3–0.8 Ma at 2 km above the valley bottom. Only one ridge crest (in the south central zone of the field area) yielded significantly older ZFT and AFT ages of ∼2 Ma; we infer that a splay of the Main Central Thrust separates this ridge from the rest of the Greater Himalaya. ZFT and AFT ages from a vertical transect along this ridge indicate exhumation rates of ∼1.5 km Myr −1 (r 2 > 0.7) from ∼2 to 0.6–0.8 Ma, whereas AHe ages indicate a faster exhumation rate of ∼2.6 km Myr −1 (r 2 = 0.9) over the last 0.8 Myr. Exhumation rates calculated for six of the remaining seven vertical profiles ranged from 1.5 to 12 km Myr −1 (all with low r 2 values of <0.6) for the time period from ∼1.2 to 0.3 Ma, with no discernible patterns in south to north exhumation rates evident. The absence of a trend in exhumation rates, despite a strong spatial gradient in rainfall, argues against a correlation of long‐term exhumation rates with modern patterns of rainfall. AFT ages in the Tethyan strata are, on average, older than in the Greater Himalaya and may be a response to a drier climate, slip on the South Tibetan Detachment, or a gentler dip of the underlying thrust ramp. These data are further evaluated with thermokinematic modeling in the companion paper by Whipp et al.