Particle production sensitive to nonfactorizable and nonperturbative processes that contribute to the underlying event associated with a high transverse momentum (pT) jet in proton+proton collisions at sqrt(s)=200 GeV is studied with the STAR detector. Each event is divided into three regions based on the azimuthal angle with respect to the highest-pT jet direction: in the leading jet direction ("Toward"), opposite to the leading jet ("Away"), and perpendicular to the leading jet ("Transverse"). In the Transverse region, the average charged particle density is found to be between 0.4 and 0.6 and the mean transverse momentum, <pT>, between 0.5 and 0.7 GeV/c for particles with pT >0.2 GeV/c at mid-pseudorapidity (|eta|<1) and jet pT >15 GeV/c. Both average particle density and <pT> depend weakly on the leading jet pT. Closer inspection of the Transverse region hints that contributions to the underlying event from initial- and final-state radiation are significantly smaller in these collisions than at the higher energies, up to 13 TeV, recorded at the LHC. Underlying event measurements associated with a high-pT jet will contribute to our understanding of QCD processes at hard and soft scales at RHIC energies, as well as provide constraints to modeling of underlying event dynamics.