Glenn was drafted in the first round (seventh overall) of the 1996 NFL Draft by the New England Patriots. Glenn immediately made a big impact for New England, recording 90 receptions for 1,132 yards and 6 touchdowns in his rookie season, and helping his team reach Super Bowl XXXI. At the time, his 90 receptions were the most ever in a single season by a rookie in NFL history. Current San Francisco 49ers receiver Anquan Boldin caught 101 passes his rookie year during the 2003 NFL Season for the Arizona Cardinals. Patriots head coach, Bill Parcells, once referred to Glenn as "she", but after the 1996 season said he was wrong and Glenn was a winner. However, Parcells left New England after Glenn's rookie season and the talented wide receiver went into a four-year stretch of personal difficulties and inconsistent play. During the 2001 season, coach Bill Belichick deactivated him for the rest of the season due to a series of off-the-field problems. Glenn only wound up playing in four games in 2001, most notably catching the first career touchdown pass thrown by Tom Brady in a game against the San Diego Chargers. The Patriots went on to win Super Bowl XXXVI without Glenn, and he did not receive a Super Bowl ring.
Before the 2003 season the Packers traded him to the Dallas Cowboys. Against the Kansas City Chiefs in 2005, he caught a touchdown pass on a flea-flicker and rushed for a touchdown on an end-around, both trick plays. Glenn finished the 2005 season with 63 receptions for 1,136 yards and 7 touchdowns, the most receiving yards he had amassed in a single season since 1999. In 2006 he recorded another 1000 yard season and 6 touchdowns.
Glenn missed the first fifteen games of the 2007 season and had been unable to even practice due to pre-season arthroscopic knee surgery. He returned to practice on December 12, 2007 but did not play in Week 15 against the Philadelphia Eagles and did not fly to Carolina for the Week 16 game. He made his season debut in Week 17 against the Washington Redskins.
Glenn was released by the Cowboys on July 25, 2008 due to health concerns on his right knee, and not signing an injury clause.
Glenn lives with his wife and one small child,a teenage son, and teenage daughter. Glenn was promoted to offensive coordinator for the Texas Revolution of the Champions Indoor Football League on April 3, 2015.