The move chews up $150,000 of the roughly $2 million worth of salary-cap space.
Jones averaged 45 yards per punt in his first full season with the Cowboys. He appeared in two games in 2011 as an injury replacement for Mat McBriar and four games in 2012 before a partially torn anterior cruciate ligament ended his season.
Jones had a 39.1-yard net average and had 30 of his 77 punts end up inside the opponents’ 20. Teams averaged only 9.2 yards per punt return against the Cowboys in 2013.
Earlier in the offseason the Cowboys signed kicker Dan Bailey to a seven-year extension worth $22.5 million.