The deal is expected to free up some salary cap space. He will make up to $4.2 million, including $750,000 in guaranteed signing bonus money, over the next three seasons, ESPN.com reported.
Jones, who has played for the Cowboys since 2011, posted a net average of 39.8 yards per punt that was 14th-best in the NFL last season. In February, the club signed Tom Hornsey to compete with him.