Hodgett-Young, who can play as a centre-half or left-back, said: "I was with the gaffer and Steve at Ilkeston a couple of seasons ago and it's great to be linking up with them again at Nuneaton.
"After they left I went to Carlton Town, but I wanted to work with them full-time again and play at a higher level.
"I'm ready for the challenge and I'm willing to put the work in to improve.
"Obviously I know a few of the Ilkeston lads who are here and I also went to the same school as Greg Tempest and Jordan Keane so I don't think I'll have a problem settling in.
"It's a step up for me, but I want to progress and help to take Nuneaton forward. I'll fight for a place in the team and show the fans that I'm committed to doing my best."
Wilson said he was happy to have the chance to work with Elliot again: "He needs to be around the first team squad and train with us so that he can progress.
"He will develop as a player with the Boro and I'm pleased to have the opportunity to help with his development and, in turn, improve the team".