Tague, 18, has scored three goals for the Gladiators this season, and has impressed the Holy Blues' boss, Curtis Woodhouse.
"James is a very talented player I’ve had my eye on for a bit," said Woodhouse.
"He has bundles of ability and if he develops how I think he will, he can be a massive player for us moving forward."
On the move, the youngster added: "It’s a fantastic opportunity for myself to play for Gainsborough Trinity and after speaking to the manager about his views on football and how he wants to take the club forward, it excited me.
"I'm looking forward to meeting the squad and playing in front of the fans. I'm excited to be part of a club moving upwards."
The club also announced that Will Thornton has extended his loan stay until the end of the season, while James Williamson is the latest player to sign for the 2020/21 season.