We have made a multifrequency (6, 3.6, and 2 cm), high-resolution (3"-6"), radio continuum survey of IRAS selected sources from the catalogue of Wouterloot & Brand (1989) to search for and study H II regions in the far outer Galaxy. We identified 31 sources in this catalog with well determined galactocentric distances, and with R approx.. greater than 15 kpc and L(sub FIR) approx.greater than 10(exp 4) solar luminosity, indicating the presence of high-mass star-formation. We have observed 11 of these sources with the Very Large Array (VLA). We observed the sources at 6 and 2 cm using "scaled arrays", making possible a direct and reliable comparison of the data at these two wavelengths for the determination of spectral indices. We detected a total of 12 radio sources, of which 10 have spectral indices consistent with optically-thin free-free emission from H II regions. Combined with previous VLA observations by other investigators, we have data on a total of 15 H II regions at galactocentric distances of 15 to 18.2kpc, among the most remote H II regions found in our Galaxy. The sizes of the H II regions range from approx. less than 0.10 to 2.3 pc. Using the measured fluxes and sizes, we determine the electron densities, emission measures, and excitation parameters of the H II regions, as well as the fluxes of Lyman continuum photons needed to keep the nebulae ionized. The sizes and electron densities are consistent with most of the sources detected in this survey being compact or ultracompact H II regions. Seven of the fifteen H II regions have sizes approx. less than 0.20 pc. Assuming simple pressure-driven expansion of the H II regions, these sizes indicate ages approx. less than 5 x 10(exp 4) yr, or only 1% of the lifetime of an O star, which implies an unlikely overabundance of O stars in the outer Galaxy. Thus, the large number of compact H II regions suggests that the time these regions spend in a compact phase must be much longer than their dynamical expansion times. Five of the fifteen H II regions have cometary shapes; the remainder are spherical or unresolved. Comparison of the radio continuum data with molecular line maps suggests that the cometary shape of the two H II regions in S 127 may be due to pressure confinement of the expanding ionized gas, as in the "blister" or "champagne flow" models of H II regions. Comparison of the radio continuum data with the IRAS far-infrared data indicates that the five most luminous H II regions are consistent with a single 0 or B star exciting a dust-free H II region. Subject headings: stars: formation - ISM: H II regions - ISM: individual objects: S 127 radio continuum: interstellar