The 25-year-old arrived at Kenilworth Road from Barnsley last January, but after suffering an early injury, has yet to make a senior appearance for the Town.
The former England Under-18 stopper has travelled north to join up with the side relegated from the Scottish Premiership at the end of last season, ahead of their opening League Cup Group Stage tie next Saturday.
Manager Rob Edwards said: “Jack was really unlucky when he first came in, but he trained extremely hard and he was the top professional, pushing Ethan Horvath and James Shea.
“He was involved in a promotion, which is great experience for him, but he’s at an age where he needs to play and with us getting promoted it becomes more difficult for him to do that here.
“Dundee United have been in contact for a while and it’s going to be a good project for him there, as they will be among the favourites to go straight back up.
“But it’s by no means the end for Jack at this football club. We just feel that this season, this is the right thing for him and we’ll be keeping in close contact in the hope it works out really well for us, Dundee United and most importantly, Jack.”
Good luck up at Tannadice, Jack!