The team now has agreements with seven of its nine picks.
Matthews, the sixth overall pick from Texas A&M, will play right tackle with the Falcons and could earn a starting job as a rookie.
Hageman, Atlanta's second-round pick, played defensive tackle at Minnesota and began work at end in last week's rookie minicamp.
The terms of the agreements were not disclosed.
The Falcons previously announced the signings of five draft picks: cornerback Ricardo Allen and linebackers Prince Shembo, Marquis Spruill, Yawin Smallwood and Tyler Starr.