  We use asteroseismic data from the Kepler satellite to determine fundamental
stellar properties of the 66 main-sequence targets observed for at least one
full year by the mission. We distributed tens of individual oscillation
frequencies extracted from the time series of each star among seven modelling
teams who applied different methods to determine radii, masses, and ages for
all stars in the sample. Comparisons among the different results reveal a good
level of agreement in all stellar properties, which is remarkable considering
the variety of codes, input physics and analysis methods employed by the
different teams. Average uncertainties are of the order of $\sim$2\% in radius,
$\sim$4\% in mass, and $\sim$10\% in age, making this the best-characterised
sample of main-sequence stars available to date. Our predicted initial
abundances and mixing-length parameters are checked against inferences from
chemical enrichment laws $\Delta Y / \Delta Z$ and predictions from 3D
atmospheric simulations. We test the accuracy of the determined stellar
properties by comparing them to the Sun, angular diameter measurements, Gaia
parallaxes, and binary evolution, finding excellent agreement in all cases and
further confirming the robustness of asteroseismically-determined physical
parameters of stars when individual frequencies of oscillation are available.
Baptised as the Kepler dwarfs LEGACY sample, these stars are the solar-like
oscillators with the best asteroseismic properties available for at least
another decade. All data used in this analysis and the resulting stellar
parameters are made publicly available for the community.
