The club have announced that any fan in possession of a valid match ticket can take up the offer, with complimentary buses departing from the Stadium of Light on the afternoon of the game.
Sunderland, who hold a 2-1 lead after the first leg of the semi-final, will also cover the cost of official supporters' branch buses, along with those from the SAFC Supporters' Association and fans organisations ALS and 73.
Black Cats chief executive Margaret Byrne said: "With such a good cup run and the congested festive fixture list, there has been a large number of games in a short space of time and we appreciate how expensive it has been for our supporters.
"We hope this gesture will help as many fans as possible to get behind Gus and the team at Old Trafford."
Sunderland anticipate they will take 150 buses to Old Trafford and they will leave the Stadium of Light at 2pm and return directly after the game.