Annual doses from external irradiation resulting from exposure to fallout from the 65 atmospheric nuclear weapons tests conducted in the Marshall Islands at Bikini and Enewetak between 1946 and 1958 have been estimated for the first time for Marshallese living on all inhabited atolls. All tests that deposited fallout on any of the 23 inhabited atolls or separate reef islands have been considered. The methodology used to estimate the radiation doses at the inhabited atolls is based on test- and location-specific radiation survey data, deposition density estimates of 137Cs, and fallout times-of-arrival provided in a companion paper (Beck et al.), combined with information on the radionuclide composition of the fallout at various times after each test. These estimates of doses from external irradiation have been combined with corresponding estimates of doses from internal irradiation, given in a companion paper (Simon et al.), to assess the cancer risks among the Marshallese population (Land et al.) resulting from exposure to radiation from the nuclear weapons tests.