When he does get back on the field, he'll find even more competition for snaps.
"There's a lot of ways Michael can help the Broncos," Rosenhaus said. "He can play fullback, halfback, he can catch the ball out of the backfield, return punts and return kicks. He's a versatile back."
Pittman, an 11th-year pro who spent his past six seasons in Tampa after four years in Arizona, rushed for 286 yards on 68 carries and caught 26 passes for 191 yards last season, when he missed six games with a high ankle sprain.
ESPN.com's John Clayton first reported the signing.
Rosenhaus said he's been in talks with the Broncos about Pittman since the start of free agency.
Henry's latest injury likely heated up those discussions.
Henry was hurt while running 100-yard sprints before the team's passing camp started last week and coach Mike Shanahan had hoped he'd return to drills on Tuesday.
"He can't go yet," Shanahan said after the workout. "Those hamstrings, you never know how long it's going to take, so I would say that chances are he'll be ready for the June camp. He will not be ready this week."
After three more workouts this week, the team returns for eight days of offseason drills over the first two weeks of June.
After signing a five-year, $22.5 million free-agent contract that included $12 million in guarantees, Henry had an injury-riddled season in Denver last year, when he rushed 167 times for 691 yards and four touchdowns.
He led the league in rushing after the first month of the season before leg injuries and off-the-field troubles took their toll. He spent several weeks fighting the NFL over a failed drug test that would have meant a one-year ban and never recovered from knee injuries as the Broncos missed the playoffs at 7-9.