NFL Network Insider Ian Rapoport reported the two sides agreed on the deal Sunday.
Rapoport reported Barkley's contract is worth $31.2 million and is fully guaranteed. The deal includes a $20.76 million signing bonus with $15 million paid immediately.
Before ever registering even one carry, Barkley becomes the fourth-highest paid running back in the league behind franchise-tagged Le'Veon Bell of Pittsburgh, Atlanta's Devonta Freeman and Buffalo's LeSean McCoy, according to spotrac.com.
In two seasons at Penn State, Barkley compiled 2,767 rushing yards, 1,034 receiving yards and 43 total touchdowns. He also was Big Ten Offensive Player of the Year in both of his seasons.
At the 2018 NFL Scouting Combine, he recorded a 4.40-second 40-yard dash, a 41-inch vertical jump and 29 reps on the bench press.