A combination of the searches for pair-produced vectorlike partners of the top and bottom quarks in various decay channels (T→Zt/Wb/Ht, B→Zb/Wt/Hb) is performed using 36.1 fb^{-1} of pp collision data at sqrt[s]=13 TeV with the ATLAS detector at the Large Hadron Collider. The observed data are found to be in good agreement with the standard model background prediction in all individual searches. Therefore, combined 95% confidence-level upper limits are set on the production cross section for a range of vectorlike quark scenarios, significantly improving upon the reach of the individual searches. Model-independent limits are set assuming the vectorlike quarks decay to standard model particles. A singlet T is excluded for masses below 1.31 TeV and a singlet B is excluded for masses below 1.22 TeV. Assuming a weak isospin (T,B) doublet and |V_{Tb}|≪|V_{tB}|, T and B masses below 1.37 TeV are excluded.