The Boise State running back was the 31st selection in the draft and is expected to share the workload as a rookie with third-year pro LeGarrette Blount.
Martin rushed for 3,431 yards and 43 touchdowns while averaging more than five yards per carry. He also had 67 receptions for 715 yards and four TDs.
He ran for 1,290 yards and 16 TDs as a senior at Boise State, capping his career with a school-record 100-yard kickoff return for a touchdown against Arizona State in the MAACO Bowl Las Vegas.
Blount rushed for more than 1,000 yards as a rookie two years ago but has yet to develop into the type of every-down running back that first-year coach Greg Schiano seeks for his offense.