The 20-year-old, who came through the youth ranks at the Madejski Stadium, had loan spells with Yeovil Town and Plymouth Argyle last season.
Shrewsbury boss Graham Turner has said that he is delighted to sign Ugwu.
"I've been chasing Gozie for some time and it's pleasing to have finally been able to secure his services," Turner told the club's official website.
"I had hoped to bring him in on loan earlier this season having watched him play for Reading's Under-21s but he did so well that night Reading wanted to hold on to him for a while longer.
"I've continued to keep a close eye on him and Gozie gives us another attacking option. He's a good addition to the squad."
Ugwu could make his debut when Shrewsbury face Port Vale on Saturday.