The FourStar galaxy evolution survey (ZFOURGE) is a 45 night legacy program with the FourStar near-infrared camera on Magellan and one of the most sensitive surveys to date. ZFOURGE covers a total of 400 arcmin2 in cosmic fields CDFS, COSMOS and UDS, overlapping CANDELS. We present photometric catalogs comprising >70,000 galaxies, selected from ultradeep Ks-band detection images (25.5–26.5 AB mag, 5σ, total), and >80% complete to Ks < 25.3–25.9 AB. We use 5 near-IR medium-bandwidth filters (J1, J2, J3, Hs, Hl) as well as broad-band Ks at 1.05–2.16 μm to 25–26 AB at a seeing of ∼05. Each field has ancillary imaging in 26–40 filters at 0.3–8 μm. We derive photometric redshifts and stellar population properties. Comparing with spectroscopic redshifts indicates a photometric redshift uncertainty σz = 0.010, 0.009, and 0.011 in CDFS, COSMOS, and UDS. As spectroscopic samples are often biased toward bright and blue sources, we also inspect the photometric redshift differences between close pairs of galaxies, finding σz,pairs = 0.01–0.02 at 1 < z < 2.5. We quantify how σz,pairs depends on redshift, magnitude, spectral energy distribution type, and the inclusion of FourStar medium bands. σz,pairs is smallest for bright, blue star-forming samples, while red star-forming galaxies have the worst σz,pairs. Including FourStar medium bands reduces σz,pairs by 50% at 1.5 < z < 2.5. We calculate star formation rates (SFRs) based on ultraviolet and ultradeep far-IR Spitzer/MIPS and Herschel/PACS data. We derive rest-frame U − V and V − J colors, and illustrate how these correlate with specific SFR and dust emission to z = 3.5. We confirm the existence of quiescent galaxies at z ∼ 3, demonstrating their SFRs are suppressed by > ×15.