Abstract We present JWST Extragalactic Medium-band Survey, the first public medium-band imaging survey carried out using JWST/NIRCam and NIRISS. These observations use ∼2 and ∼4 μm medium-band filters (NIRCam F182M, F210M, F430M, F460M, F480M; and NIRISS F430M and F480M in parallel) over 15.6 arcmin² in the Hubble Ultra Deep Field (UDF), thereby building on the deepest multiwavelength public data sets available anywhere on the sky. We describe our science goals, survey design, NIRCam and NIRISS image reduction methods, and describe our first data release of the science-ready mosaics, which reach 5σ point-source limits (AB mag) of ∼29.3–29.4 in 2 μm filters and ∼28.2–28.7 at 4 μm. Our chosen filters create a JWST imaging survey in the UDF that enables novel analysis of a range of spectral features potentially across the redshift range of 0.3 < z < 20, including Paschen-α, Hα+[N ii], and [O iii]+Hβ emission at high spatial resolution. We find that our JWST medium-band imaging efficiently identifies strong line emitters (medium-band colors >1 mag) across redshifts 1.5 < z < 9.3, most prominently Hα+[N ii] and [O iii]+Hβ. We present our first data release including science-ready mosaics of each medium-band image available to the community, adding to the legacy value of past and future surveys in the UDF. This survey demonstrates the power of medium-band imaging with JWST, informing future extragalactic survey strategies using JWST observations.