Jones attended Catholic High School in Baton Rouge, Louisiana, and was a letterman in football. In football, he won All-District honors as a Punter/Tight End and All-State honors as a punter. Jones graduated from Catholic High School in 1999. He averaged more than nine punts per game and never recorded any injury or fatigue.

Jones was drafted in the seventh-round (224th overall) by the Seattle Seahawks in the 2004 NFL Draft. He was one of three punters to be selected that year. He played in six games with Seahawks in between stints on the practice squad during his rookie season. He shared punting duties with Tom Rouen and Ken Walter during the season. On the year, Jones punted 26 times for a 38.0 average with a net of 32.2, six inside-the-20 and two touchbacks. He had a season long with a 51-yard punt against the Carolina Panthers on October 31. On November 14 at the St. Louis Rams, he punted three times for a 49.3-yard gross average and a net of 42.7, when he had another 51-yard punt.

Jones was awarded off waivers to the Miami Dolphins on July 25, 2005. He was released following training camp and re-signed to the practice squad, but was placed on the active roster prior to the season opener. He went on to play in all 16 games in his first season with the Dolphins. On the season, he had 88 punts for a 43.5-yard average, including a net of 39.3, which led the NFL and marked a new Dolphins’ single-season record. He also added 31 punts inside-the-20, which ranked second in the AFC and was a Dolphins’ single-season record as well. Of his 88 punts, 24 went 50 yards or longer, with three traveling 60 yards or longer. He had a punt of 50 yards or longer in all but three games, and had a net average of 40.0 or better in nine games. He also held for placekicker Olindo Mare throughout the season. Jones’ performance during the season earned him a selection as a third alternate for the Pro Bowl.

Jones experienced a bit of regression in 2006 compared to the previous year. For the season, he had 85 kicks for 3,640 yards – an average of 42.8 yards per kick. He also had a net average of 35.7 yards per punt, with 28 punts inside the 20-yard line. He had one punt blocked during the season.

Jones was a restricted free agent in the 2007 offseason. He was tendered a contract by the Miami Dolphins on March 2.

On April 13, the St. Louis Rams signed Jones to an offer sheet. Less than a week later, Dolphins general manager Randy Mueller announced that the team would not match the offer sheet and Jones became property of the Rams in exchange for the 225th pick in the 2007 NFL Draft. The contract was worth $5.585 million over five years. It included a signing bonus of $1.175 million and salaries of $510,000 in 2007, $700,000 in 2008, $1 million in 2009, $1.1 million in 2010, and $1.1 million in 2011.

In 2007, Jones broke the Rams record for highest punting average in a single season, punting 78 times for a 47.2-yard punting average. The previous record of 45.5-yard punting average lasted 45 years after being set in 1962 by Danny Villanueva. In 2008, he became the first NFL punter to average at least 50 yards per punt since Sammy Baugh in 1940. He was voted second-team All-Pro and a first alternate to the Pro Bowl. For the second straight year, he was voted an alternate to the Pro Bowl in 2009. In 2009, he broke the Rams career gross average punt record with a 48.0-yard average, surpassing the 44.3-yard average established by Danny Villanueva from 1961 to 1964. In the 2010 season, he finished with 94 punts for 4,276 net yards for a 45.49 average. In the 2011 season, he finished with 105 punts for 4,652 net yards for a 44.30 average.

Jones signed a one-year contract with the Houston Texans on March 29, 2012. He was expected to compete with and briefly replace Brett Hartmann as punter while Hartmann served his three-game suspension, but took over as the full-time punter when Hartmann was released. In the 2012 season, he finished with 88 punts for 4,150 net yards for a 47.16 average.

On March 25, 2013, Jones signed with the Philadelphia Eagles. On March 11, 2014, Jones re-signed with the Eagles on a three-year deal worth a maximum of $6 million. During the 2013 season, he set a franchise record for net punting average with 40.4 yards. In the 2014 season, he finished with 76 punts for 3,331 net yards for a 43.83 average. In the 2015 season, he finished with 86 punts for 4,038 net yards for a 46.95 average.

On November 18, 2016, Jones signed a three-year, $5.5 million contract extension with the Eagles through 2019. Overall, in the 2016 season, he finished with 63 punts for 2,888 net yards for a 45.84 average.

In the 2017 season, Jones finished with 67 punts for 3,033 net yards for a 45.27 average. He earned a Super Bowl ring when the Eagles defeated the New England Patriots 41-33 in Super Bowl LII. Jones recorded the only punt in the game that went 41 yards. During his time with the Eagles, Jones set the all-time Eagles gross punting average record with 45.4 yards, punts inside the 20-yard line with 138, and all-time net punting average with 40.5 yards.

On February 27, 2018, Jones announced his retirement from the NFL. On April 4, 2018, Jones requested and was granted his release from the Eagles’ reserve/retired list, making him a free agent, citing his desire to play again.

On October 2, 2018, Jones signed with the Los Angeles Chargers after the team released Drew Kaser.