The bright Magellanic irregular galaxy NGC 4449 was observed during the Astro-2 Space Shuttle mission by the Ultraviolet Imaging Telescope (UIT), which obtained images of a ~40 arcmin field centered on the galaxy in two broad far-ultraviolet (FUV) bands centered at 1520 A and 1620 A, with 3 arcsec - 5 arcsec spatial resolution. Together with H-alpha and H-beta fluxes from ground-based Fabry-Perot images, these data are analyzed in order to explore the recent star formation history of NGC 4449. Maps of the flux ratios H-alpha/FUV and FUV/blue continuum are presented and interpreted using evolutionary synthesis models. Photometry is presented both for 22 apertures containing large OB complexes and for 57 small apertures containing compact FUV-emitting knots. The OB complexes along the northern edge of the visible system have high H-alpha/FUV ratios, and thus appear to be more dominated by the current generation of stars than are other parts of the galaxy. However, young sources do exist elsewhere and are particularly conspicuous along the bar. The small aperture analysis shows three candidate regions for sequential star formation. Surface brightness profiles are consistent with an exponential disk in both the FUV and the optical continuum.