Harrison moves to League Two Shrewsbury on a season-long loan.
The 19 year-old enjoyed an impressive six-month spell with Chester in the National League North in 2024/25.
Shrewsbury director of football Micky Moore said: "I'm really excited that we've signed Elyh.
"He's someone we've targeted since last season ended and I think he's got a bright future.
"We watched him play at Chester last year and continued to watch him when he went back to play for United's under-21s.
"We think he's got all the right characteristics and that this could be a very good loan for him.
"Michael (Appleton) wanted to get him in the building as soon as possible, so I'm really happy to get it over the line because it was a tough process due to the amount of interest in the player.
"But I want to thank Elyh and Man United for their help throughout.
"I'm excited to see how he develops throughout the season."