In this work, we calculate with ab initio methods the current-voltage characteristics for ideal single- and double-barrier Fe/MgO (001) magnetic tunnel junctions. The current is calculated in the phase-coherent limit by using the recently developed SMEAGOL code, combining the nonequilibrium Green function formalism with density-functional theory. In general we find that double-barrier junctions display a larger magnetoresistance, which decays with bias at a slower pace than their single-barrier counterparts. This is explained in terms of enhanced spin filtering from the middle Fe layer sandwiched in between the two MgO barriers. In addition, for double-barrier tunnel junctions, we find a well defined peak in the magnetoresistance at a voltage of V=0.1V. This is the signature of resonant tunneling across a majority quantum well state. Our findings are discussed in relation to recent experiments.