"I'm excited to be back to coaching again, to be again be part of something that is bigger than myself," Bradley, 57, said in a phone interview with ESPN.com.
Added coach Dana Holgorsen in a statement: "Tom brings numerous years of successful college coaching experience and versatility. He is an excellent defensive teacher, has high energy and intensity and gives us a proven recruiter with regional and national ties."
Bradley coached for 33 years under Paterno at Penn State after graduating from there in 1979.
After coaching various positions, he eventually replaced Jerry Sandusky as defensive coordinator in 2000. When Sandusky was charged with sexually abusing children, Bradley took over for Paterno as interim head coach in Penn State's last four games in 2011.
He resigned from the school after the season, and has spent the last three years as a football analyst, most recently covering Army football games.
"The time away, it was hard, but I did some interesting stuff," Bradley said. "I enjoyed it. It was something new to learn and a new challenge. But I'm a coach. That's what I do. That's what I love and I'm excited to have the opportunity to work as a coach again and be around student-athletes again.''
While at Penn State, Bradley was successful both as a coordinator and a recruiter. From 2004 to '09, he coached the Nittany Lions to six straight top 15 finishes in total and scoring defense nationally. He was an assistant on two national championship teams and coached in 26 bowl games.
Holgorsen said he would designate Bradley's defensive coaching position at a later date.
"We haven't talked about the specifics yet, but I'm sure I'll be involved in Pennsylvania," Bradley said of recruiting efforts. "I know the lay of the land. It's not that far from where I'm from. It's good to be able to be home.''
Earlier Friday, Holgorsen confirmed the promotion of safeties coach Tony Gibson to defensive coordinator.
Bradley said he and Gibson developed a strong relationship while competing for players on the recruiting trail.
"Tony Gibson and I have recruited against each other in Pennsylvania for a lot of years, and it will be good to finally be on his side," Bradley said in a statement. "I look forward to working with my friend to build a strong defensive unit at West Virginia."