In Saturday night's match, the Argentinean player unleashed a commanding shot into the upper corner of the net, as City dominated chances against the team that secured fourth place in last season's standings.
The 36-year-old has signed a two-year contract with the option of that being extended for a further year, the Manchester United website said on Tuesday evening
Pogba created space for himself just outside the corner of the penalty area and bent a powerful shot past Fulham goalkeeper Alphonse Areola and into the far corner of the net in the 65th minute
The midfielder was sent off in the 70th minute for a second yellow card after his challenge on former United midfielder Ander Herrera just after United had gone 2-1 down when Marquinhos scored.
