XENONnT is a dark matter direct detection experiment , utilizing 5.9 t of instrumented liquid xenon , located at the INFN Laboratori Nazionali del Gran Sasso . In this work , we predict the experimental background and project the sensitivity of XENONnT to the detection of weakly interacting massive particles ( WIMPs ) . The expected average differential background rate in the energy region of interest , corresponding to ( 1 , 13 ) keV and ( 4 , 50 ) keV for electronic and nuclear recoils , amounts to 13.1 \pm 0.6 \si ( keV.t.y ) ^-1 and ( 2.2 \pm 0.5 ) \times 10 ^ { -3 } \si ( keV.t.y ) ^-1 , respectively , in a 4 t fiducial mass . We compute unified confidence intervals using the profile construction method , in order to ensure proper coverage . With the exposure goal of 20 \si t.y , the expected sensitivity to spin-independent WIMP-nucleon interactions reaches a cross-section of 1.4 \times 10 ^ { -48 } \mathrm { cm } ^ { 2 } for a 50 GeV/c ^ { 2 } mass WIMP at 90 % confidence level , more than one order of magnitude beyond the current best limit , set by XENON1T . In addition , we show that for a 50 GeV/c ^ { 2 } WIMP with cross-sections above 2.6 \times 10 ^ { -48 } \mathrm { cm } ^ { 2 } ( 5.0 \times 10 ^ { -48 } \mathrm { cm } ^ { 2 } ) the median XENONnT discovery significance exceeds 3 \sigma ( 5 \sigma ) . The expected sensitivity to the spin-dependent WIMP coupling to neutrons ( protons ) reaches 2.2 \times 10 ^ { -43 } \mathrm { cm } ^ { 2 } ( 6.0 \times 10 ^ { -42 } \mathrm { cm } ^ { 2 } ) .