  By using lattice QCD computations we determine the sigma terms and
strangeness content of all octet baryons by means of an application of the
Hellmann-Feynman theorem. In addition to polynomial and rational expressions
for the quark mass dependence of octet members, we use SU(3) covariant baryon
chiral perturbation theory to perform the extrapolation to the physical up and
down quark masses. Our N_f=2+1 lattice ensembles include pion masses down to
about 190 MeV in large volumes (M_\pi L > 4), and three values of the lattice
spacing. Our main results are the nucleon sigma term \sigma_{\pi N} =
39(4)(^{+18}_{-7}) and the strangeness content y_{N} = 0.20(7)(^{+13}_{-17}).
Under the assumption of validity of covariant baryon \chi PT in our range of
masses one finds y_{N} = 0.276(77)(^{+90}_{-62}).
