The 21-year-old Manchester United centre-back joined the Cumbrians in the summer and has impressed for the League One side, scoring four goals in 23 matches.
His form has caught the eye of Tigers boss Nigel Pearson, who will land Chester on Tuesday to add to the signings of Aaron Mclean and Matt Fryatt.
Carlisle boss Greg Abbott told his club's official website: "I found out late last night (Sunday) that James was heading for Hull and we have to send him with all our best wishes.
"Manchester United thanked us for the way we have developed their player and it has turned out to be an excellent move for him.
"Obviously we don't want him to go but this is a fantastic opportunity for him. He has been excellent for us and we will all be looking out for him and hoping that he does well in the future."