We study radiative processes of uniformly accelerated entangled atoms, interacting with an electromagnetic field prepared in the Minkowski vacuum state. We discuss the structure of the rate of variation of the atomic energy for two atoms travelling in different hyperbolic world lines. We identify the contributions of vacuum fluctuations and radiation reaction to the generation of entanglement as well as to the decay of entangled states. Our results resemble the situation in which two inertial atoms are coupled individually to two spatially separated cavities at different temperatures. In addition, for equal accelerations we obtain that one of the maximally entangled antisymmetric Bell state is a decoherence-free state.