A native of New Britain, Connecticut, Reed attended New London High School. As a junior, he completed 122 of 222 passes for 1,706 yards and 38 touchdowns. He threw only two interceptions, and also rushed for 370 yards and eight touchdowns. He led New London to an undefeated regular season in 2007, and was a finalist for the 2008 Joe Montana High School Quarterback of the Year. Considered a four-star recruit by Rivals.com, he was rated the 10th best dual-threat quarterback in the nation.
Reed accepted an athletic scholarship to attend the University of Florida, where he played for coach Urban Meyer and coach Will Muschamp's Florida Gators football teams from 2009 to 2012. Originally recruited as a quarterback, he did not appear in any games and was redshirted as a true freshman in 2009. After the 2009 season, he shifted to the tight end position. Reed finished his college career with 78 receptions for 938 yards and six touchdowns. He decided to forgo his final season of college eligibility, and enter the NFL Draft after the 2012 season.
Reed was drafted in the third round, 85th overall pick, by the Washington Redskins in the 2013 NFL Draft. On May 24, 2013, he officially signed a four-year rookie contract with the team.
On September 15, 2013, Reed recorded his first career touchdown against the Green Bay Packers. This touchdown made him the first Redskins rookie to score a touchdown in the first two games of his career since retired tight end Chris Cooley in 2004. On October 20, 2013, Reed recorded a career-high nine receptions for a career-high 134 yards and a touchdown against the Chicago Bears, setting a new Redskins franchise record for receiving yards by a rookie tight end, as well as recording his first 100-plus yard game. On November 11, 2013, Reed was pulled out of the game early after suffering a concussion in a game against the Philadelphia Eagles. After missing four consecutive games due to headaches after the concussion, he was placed on injured reserve on December 19, 2013. Despite playing only nine games, with four starts, in his first season, Reed was named to Pro Football Weekly/Pro Football Writers of America all-rookie team.
On September 7, 2014, Reed exited the season opener against the Houston Texans with a hamstring injury. Reed was sidelined for four more games until Week 6. On October 12, 2014, Reed caught eight passes for 92 yards against the Arizona Cardinals. On November 16, 2014, Reed suffered another hamstring injury during the game against the Tampa Bay Buccaneers. The injury sat Reed out for Week 12 game against the San Francisco 49ers. On November 30, 2014, Reed caught nine passes for a 123 yards against the Indianapolis Colts, for his second 100-plus game of his career.
On September 13, 2015, Reed caught seven passes for 63 yards and his first touchdown of the season against the Miami Dolphins, a four-yarder. On October 25, 2015, Reed caught a career-high 11 passes for 72 yards and a career-high two touchdowns against the Tampa Bay Buccaneers. The touchdowns were from 3 and 6 yards out, respectively. On November 15, 2015, Reed caught two more touchdowns against the New Orleans Saints, a 16-yard reception and an 8-yard reception. On November 29, 2015, Reed caught 8 passes for 98 yards against the New York Giants. On December 13, 2015, Reed caught 9 passes for 120 yards and a touchdown against the Chicago Bears for his 3rd 100-plus yard game of his career. On December 20, 2015, Reed caught 7 passes for 84 yards against the Buffalo Bills. Reed caught two touchdowns for the 3rd time this season, one from 3 yards out, and the other from 18 yards out. On December 26, 2015, Reed recorded 129 yards off of nine receptions and two touchdowns against the Philadelphia Eagles to win the NFC East. In his first playoff game, Reed recorded nine passes for 120 yards and one touchdown against the Green Bay Packers. He was ranked 77th on the NFL Top 100 Players of 2016.
On May 5, 2016, Reed signed a five-year contract extension, worth $50 million, including $22 million guaranteed. On October 2, 2016, Reed caught nine passes for 73 yards and two touchdowns against the Cleveland Browns. Reed scored two touchdowns in a single game for the 5th time in his career. Reed became the fastest tight end in NFL history to reach 200 career receptions. On October 13, 2016, Reed was diagnosed with a concussion and was sidelined for two games until Week 8. On October 30, 2016, Reed caught nine passes for 99 yards and a touchdown against the Cincinnati Bengals, his 17th touchdown of his career. On November 20, 2016, Reed caught five passes for 79 yards against the Green Bay Packers. Reed's 231 career receptions passed Rod Gardner (227) for 15th on the Redskins' all-time receptions list. On November 24, 2016, Reed caught a season-high ten passes for 95 yards and two touchdowns against the Dallas Cowboys. Reed recorded a 5-yard touchdown and an 8-yard touchdown, scoring his fourth and fifth touchdown of the season (18th and 19th career). During the game, Reed suffered a Grade 3 AC joint separation in his left shoulder, keeping him out of the Week 13 matchup against the Arizona Cardinals. On December 20, 2016, in a Monday Night Football game against the Carolina Panthers (in which Washington lost to Carolina), Reed was ejected after punching Panthers safety Kurt Coleman in the helmet; the subsequent penalty pushed Washington out of the red zone and forced them to make a field goal instead. On December 20, 2016, Reed was named to the 2017 Pro Bowl roster, which was his first career Pro Bowl nomination.
Reed is the younger brother of wide receiver David Reed, who was drafted in the fifth round of 2010 NFL Draft by the Baltimore Ravens.