The 22-year-old Klefbom will earn $4.167 million each season throughout the life of the contract, ESPN's Craig Custance reports.
The reported $29.17-million deal is expected to be finalized in the next few days.
It's a significant investment in a player with less than a full season of NHL experience, but also a tremendous vote of confidence. General manager Peter Chiarelli likely envisions Klefbom as a key building block and a major part of the team's future, and that the annual hit will be reasonable during his prime.
The Swede scored two goals and 20 points in 60 games for Edmonton last season and, despite spending time in the AHL, was entrusted with the second-highest average ice time per game among Oilers skaters.