The azimuthal variation of jet yields in heavy-ion collisions provides information about the path-length dependence of the energy loss experienced by partons passing through the hot, dense nuclear matter known as the quark-gluon plasma. This paper presents the azimuthal anisotropy coefficients v2, v3, and v4 measured for jets in Pb+Pb collisions at sNN=5.02 TeV using the ATLAS detector at the LHC. The measurement uses data collected in 2015 and 2018, corresponding to an integrated luminosity of 2.2 nb-1. The vn values are measured as a function of the transverse momentum of the jets between 71 and 398 GeV and the event centrality. A nonzero value of v2 is observed in all but the most central collisions. The value of v2 is largest for jets with lower transverse momentum, with values up to 0.05 in mid-central collisions. A smaller, nonzero value of v3 of approximately 0.01 is measured with no significant dependence on jet pT or centrality, suggesting that fluctuations in the initial state play a small but distinct role in jet energy loss. No significant deviation of v4 from zero is observed in the measured kinematic region.