An extended theory is presented for the calculation of neutral-beam-driven currents in tokamaks, including for the first time the effects of radial transfer of toroidal momentum, background ion rotation, and fast beam ion pressure gradients. The new theory contains the beam current, electron return current with trapping effects, and the bootstrap current contributions of previous theories, but it is extended to be consistent with particle and momentum balance and ambipolarity in a rotating plasma with the radial transfer of toroidal momentum and a significant fast beam ion population. These new effects can produce order unity changes in the beam-driven and bootstrap currents in a Tokamak Fusion Test Reactor (TFTR) model problem.