"I'm delighted to come here to play league football, and showcase what I can do," he told BBC Radio Shropshire.
Last season, he had loan spells at Swindon and Rochdale, helping Dale win promotion from League Two.
"I hope I can do that again with Shrewsbury," he added.
"Graham Turner sold the place to me, but I know Shrewsbury are a good club with a good stadium, who are doing well in League Two."
Obadeyi started as a junior at Coventry and joined Bolton in 2008 ahead of a number of high-profile clubs.
Shrews boss Turner said: "He's a big strong lad, he's quick, and he can play in a number of positions. He's a useful addition to our squad."
Source: BBC Sport
Source: BBC Sport