This comes just a week after Jones signed his restricted free agent tender.
According to Jason Fitzgerald, the Cowboys freed up $542,000 in cap room with this extension.
Jones, 25, was 14th in the league in terms of net punting average (39.8 yards) last season and 20th in average return yards per punt (9.6 yards). Pro Football Focus has Jones rated as the No. 15 punter in the league out of 37 qualifying players.