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We describe the sources of stray light and thermal background that affect JWST observations, report actual backgrounds as measured from commissioning and early-science observations, compare these background levels to prelaunch predictions, estimate the impact of the backgrounds on science performance, and explore how the backgrounds probe the achieved configuration of the deployed observatory. We find that for almost all applications, the observatory is limited by the irreducible astrophysical backgrounds, rather than scattered stray light and thermal self-emission, for all wavelengths lambda < 12.5 micron, thus meeting the level 1 requirement. This result was not assured given the open architecture and thermal challenges of JWST, and it is the result of meticulous attention to stray light and thermal issues in the design, construction, integration, and test phases. From background considerations alone, JWST will require less integration time in the near-infrared compared to a system that just met the stray-light requirements; as such, JWST will be even more powerful than expected for deep imaging at 1-5 micron. In the mid-infrared, the measured thermal backgrounds closely match prelaunch predictions. The background near 10 micron is slightly higher than predicted before launch, but the impact on observations is mitigated by the excellent throughput of MIRI, such that instrument sensitivity will be as good as expected prelaunch. These measured background levels are fully compatible with JWST's science goals and the Cycle 1 science program currently underway.