Measurements of the cross section for the production of top quark pairs in association with a pair of jets from bottom quarks (σtt¯bb¯¯¯) and in association with a pair of jets from quarks of any flavor or gluons (σtt¯jj) and their ratio are presented. The data were collected in proton-proton collisions at a center-of-mass energy of 13 TeV by the CMS experiment at the LHC in 2016 and correspond to an integrated luminosity of 35.9 fb−1. The measurements are performed in a fiducial phase space and extrapolated to the full phase space, separately for the dilepton and lepton+jets channels, where lepton corresponds to either an electron or a muon. The results of the measurements in the fiducial phase space for the dilepton and lepton+jets channels, respectively, are σtt¯jj = 2.36±0.02 (stat)±0.20 (syst) pb and 31.0±0.2 (stat)±2.9 (syst) pb, and for the cross section ratio 0.017 ± 0.001 (stat) ± 0.001 (syst) and 0.020 ± 0.001 (stat) ± 0.001 (syst). The values of σtt¯bb¯¯¯ are determined from the product of the σtt¯jj and the cross section ratio, obtaining, respectively, 0.040±0.002 (stat)±0.005 (syst) pb and 0.62±0.03 (stat)±0.07 (syst) pb. These measurements are the most precise to date and are consistent, within the uncertainties, with the standard model expectations obtained using a matrix element calculation at next-to-leading order in quantum chromodynamics matched to a parton shower.