The teenager was said to be in a critical condition on Sunday night.
Costello was airlifted to Leeds General Infirmary after suffering an injury during an Under-19s game against Salford on Saturday.
A statement from the Giants read: "It is with regret that Huddersfield Giants wish to inform everyone of the passing of 17-year-old academy player Ronan Costello.
"The club have been asked by the family to send their thanks for the messages of support they have received to date and have requested that all well-wishers now allow them to grieve and respect their privacy.
"The Huddersfield Giants are collating all messages, cards and tweets that they receive to pass to the family at the appropriate time."
The youngster's family said in a statement: "We are absolutely devastated to lose Ronan so tragically and suddenly.
"Ronan was a loving and caring 17-year-old lad who was dedicated to his family and friends. He was a credit to all of his family and we are so proud of him and his achievements. We are all truly heartbroken and Ronan will be missed and forever in our hearts."
Costello had never made an appearance for the senior team.