Norwood was lightly recruited out of State College Area High School. He received few scholarship offers and accepted Penn State's last minute offer over an offer from Bucknell to play football and basketball. His leadership and jumping skills on the basketball court was what led coach Joe Paterno to offer him a football scholarship. In 2005, his freshman season, Norwood caught 32 passes for 422 yards with a 13.2 yard average. Norwood's sophomore season concluded with him making the Dean's List and being named to the Academic All-Big Ten team. He caught 45 passes for 472 yards and 2 touchdowns with a 10.5 yard average. He joined the basketball team under Ed DeChellis in January, practicing regularly and appearing in four games as a reserve guard in his only season playing basketball. In his junior season, Jordan caught 40 balls for 484 yards and 5 touchdowns with a 12.1 yard average including catching a touchdown pass lying down on the ground versus Buffalo. He had a season high 8 catches for 65 yards and a touchdown in a 36-31 win over Indiana. Norwood earned all-Big Ten honorable mention honors as a senior, after catching 41 passes for 637 yards and six touchdowns. Norwood's eight-catch, 116-yard performance versus Oregon State on September 6, 2008 moved him past O. J. McDuffie into third place on Penn State's career reception list. Afterward, he was congratulated in person by McDuffie, who attended the game. Norwood had a second consecutive 100 plus yard game on September 13, 2008 against the Syracuse Orange. He had 5 receptions for 113 yards and two touchdowns. Before the game against Illinois, Norwood injured his hamstring and didn't participate in the games against the Illini and the Boilermakers.
After being undrafted in the 2009 NFL Draft, Norwood signed with the Cleveland Browns as an undrafted free agent on May 1, 2009. He was waived by the Browns during final roster cuts on September 5, 2009.
Philadelphia Eagles
On September 23, 2009, Norwood was signed to the Philadelphia Eagles practice squad. He was promoted to the active roster on December 1, 2009. He was waived on December 7. On December 9, he was re-signed to their practice squad. He was re-signed to a three-year contract on January 11, 2010. On March 18, Norwood changed his number from 84 to 19 after Hank Baskett was re-signed by the Eagles and took number 84 back. Norwood was waived on September 4.
Cleveland Browns (second stint)
Norwood was signed to the Cleveland Browns' practice squad on September 6, 2010. He was promoted to the active roster before Week 13 of the 2010 season. He was waived on August 25, 2013.
Tampa Bay Buccaneers
On August 28, 2013, Norwood signed with the Buccaneers. On August 31, 2013, he was cut by the Buccaneers.
Denver Broncos
Norwood signed with the Denver Broncos during the 2014 offseason. The Broncos placed Norwood on injured reserve on August 25, 2014 after he tore his ACL. On February 7, 2016, Norwood was part of the Broncos team that won Super Bowl 50. In the game, the Broncos defeated the Carolina Panthers by a score of 24–10. In the game, Norwood set a Super Bowl record for the longest punt return at 61 yards. The return set up a field goal that put the Broncos up 13–7. On March 23, 2016, Norwood signed a one-year contract with the Denver Broncos after drawing interest from the New York Jets and Detroit Lions.
Retirement
On September 10, 2017, Norwood announced his retirement from the NFL.
