Brooks was a linebacker with Tampa Bay; Dungy coached Tampa Bay and Indianapolis, leading the Colts to a Super Bowl title in 2007; Harrison was a receiver for Indianapolis; and Jones was an offensive tackle with Seattle.
Former New York Giants defensive end Michael Strahan also was selected a modern-era finalist along with defensive end/linebacker Charles Haley, defensive end/linebacker Kevin Greene, receiver Andre Reed, running back Jerome Bettis, receiver/returner Tim Brown, safety John Lynch, guard Will Shields, cornerback/safety Aeneas Williams, kicker Morten Andersen and former San Francisco owner Edward DeBartolo Jr.
Punter Ray Guy and defensive end Claude Humphrey were announced as senior nominees in August.
The 46-member selection committee will vote Feb. 1 in New York, with a minimum 80 percent required for induction.
Former NFL Commissioner Paul Tagliabue failed to advance. Former coaches Jimmy Johnson and Don Coryell and general manager George Young also dropped out along with fellow semifinalists Steve Atwater, Roger Craig, Terrell Davis, Joe Jacoby, Karl Mecklenburg and Steve Wisniewski.
Strahan, Andersen and Lynch are in their second years of eligibility. Shields is in his third year, Bettis -- an ESPN NFL analyst -- his fourth, Brown and Williams their fifth, Reed his ninth, and Greene and Haley their 10th.
The modern-era finalists were chosen by the selection committee from a list of 126 nominees that was reduced to 25 semifinalists. Each finalist received a minimum vote of 80 percent.
To be eligible, modern-era players and coaches must have last played or coached more than five seasons ago.
If selected, Guy would become the first punter to be inducted. Andersen would become the second pure kicker, following Jan Stenerud.
Information from The Associated Press was used in this report.