The new contract, which will keep Morais at the Coral Windows Stadium until the end of June 2017, should be officially ratified by The Football Association and Football League tomorrow (Tuesday).
Morais' current City contract expired after Saturday's 3-3 draw in the F.A Cup at Championship side Millwall.
Having made 23 appearances for the Bantams so far this season, Morais has been an increasingly important member of Phil Parkinson's squad over the last few months.
The Portuguese performer has started nine of City's last ten matches, scoring three goals and setting up two further goals during that period.