Originally from Middletown, Connecticut, Tye was a standout tight end/kick returner at Xavier High School in Middletown. Tye then did his final year of high school at Salisbury School where he was labeled a three-star recruit by Rivals and Scout.com and was recognized as the No. 6 prospect in Connecticut and No. 19 tight end in the nation by the latter.
After going undrafted in the 2015 NFL Draft, Tye was signed by the New York Giants as an undrafted free agent. He competed with Larry Donnell, Adrien Robinson, Daniel Fells and Jerome Cunningham for the tight end job. On September 1, 2015, he was waived by the Giants. On September 7, 2015, he was signed to the Giants' practice squad. On October 3, 2015, the Giants promoted Tye to the active roster. Tye became the first player from Stony Brook to play in the NFL. On December 14 during a Monday Night Football game against the Miami Dolphins, Tye caught his first NFL touchdown from quarterback Eli Manningen route to a Giants victory. In the Giants next game against the Carolina Panthers on December 20, Tye found the endzone again in a Giants loss to the undefeated Carolina Panthers. In the season finale on January 3, 2016, Tye found the endzone again in a Giants loss to the Philadelphia Eagles. For the 2015 season, Tye had 42 receptions for 464 yards and three touchdowns in 13 games played. Following the season, Tye was named to the 2015 PFWA All-Rookie Team. Going into the 2016 season, Tye still had to prove his worth. He made the final 53-man roster and started the 2016 season on the Giants active roster. Tye's statistics regressed in 2016 as he recorded 48 receptions for 395 yards and only one touchdown. On February 15, 2017, Tye re-signed with the Giants on a one-year deal. On September 2, 2017, the day of final roster cuts, Tye was released by the Giants.
Tye was claimed off waivers by the New York Jets on September 3, 2017. On September 10, Tye made his Jets debut, recording three receptions for 34 yards in the 21–12 loss to the Buffalo Bills. He was released on October 3, 2017.
On October 12, 2017, Tye was signed to the New England Patriots' practice squad. He signed a reserve/future contract with the Patriots on February 6, 2018. On September 1, Tye was waived with an injury designation as part of the roster cutdown, and reverted to the team's injured reserve the next day. He was released on September 6, 2018.
Philadelphia Eagles
On November 13, 2018, Tye was signed to the Philadelphia Eagles practice squad. Tye signed a reserve/future contract with the Eagles on January 14, 2019. He was released during final roster cuts on August 30, 2019.
Personal life
During his rookie season in 2015, Tye earned the nickname "Baby Gates" because of his admiration of San Diego Chargers tight end Antonio Gates and the fact that Tye and Gates have similar playing styles.