He won the 2014 NCAA Division I men's ice hockey tournament as a first year and was a Hobey Baker Award finalist as a senior.

[5] In his freshman year at Union, Vecchione led the team rookies in scoring with 34 points in 38 games and ranked fourth across the ECAC.

On February 3, 2017, Vecchione became Union's all time Division I leading scorer when he recorded his 158th and 159th career point in a 5–3 loss to Cornell.

[15] As a result of his breakout season, Vecchione was named a Hobey Baker Award finalist and the ECAC Hockey Player of the Year.

[16] He was also named to the All-ECAC Hockey First Team and won Union's William M. Jaffe Award for most outstanding male student-athlete.

[19] On July 1, 2017, Vecchione, as a restricted free agent, accepted a two-year, two-way deal to continue with the Philadelphia Flyers.

[20] On September 27, 2017, he was loaned to the Flyers American Hockey League (AHL) affiliate, the Lehigh Valley Phantoms to play the 2017–18 season.

[24] After parts of three seasons in the Flyers organization, Vecchione left as a free agent to sign on a one-year, two-way contract with the St. Louis Blues on July 1, 2019.

[25] He attended the Blues 2019 training camp, before he was placed on waivers and assigned to the AHL to join affiliate, the San Antonio Rampage for the 2019–20 season.