2009-10: Jeremy Welsh played in 39 games for Union College as a freshman. He scored 10 goals with 9 assists and had an even plus/minus with 45 penalty minutes.
2010-11: Welsh was the second-leading scorer for Union College in his sophomore season. In 40 games he scored 16 goals with 21 assists and was -2 with 34 penalty minutes. Union finished first in ECAC Hockey in the regular season and received an at-large bid to the NCAA Tournament after falling to Colgate in an ECAC quarterfinal series. The Dutchmen lost to Minnesota-Duluth, 2-0, in the NCAA East Regional semifinals.
2011-12: Welsh was signed by the Hurricanes as a free agent following his junior season at Union College after the Dutchmen won the ECAC Hockey championship and reached the Frozen Four for the first time in school history. He made his NHL debut in an April game against Florida and was scoreless with 4 penalty minutes in 16:32 of ice time in his only NHL appearance. Welsh scored 27 goals with 17 assists and was plus-18 with 47 penalty minutes in 40 games for Union. He was named to the NCAA East Second All-Star Team and was the ECAC Hockey tournament MVP. Welsh was tendered a qualifying offer by the Hurricanes in June and signed to a two-year contract in September, 2012.
2012-13: Welsh appeared in five games with the Hurricanes in his first pro season; spending most of the year with Carolina's AHL affiliate in Charlotte. He had 1 assist and was +1 in limited ice time with the Hurricanes. Welsh played 69 games for the Checkers, scoring 14 goals with 12 assists, and was -9 with 16 penalty minutes. Charlotte finished second in the South Division and lost to third-place Oklahoma City in a first round playoff series. Welsh had 3 assists and was -4 with 2 penalty minutes in five playoff games.
A big bodied center, Welsh was a point per game player during his last two years in the NCAA and performed admirably during his lone season in the AHL. Perhaps a late bloomer, Welsh has limited time to convince a team he can stick around the big leagues.
Welsh was dealt by the Carolina Hurricanes to the Vancouver Canucks prior to the start of the 2013-14 season, in a deal that also saw Hurricanes prospect Zac Dalpe sent to the Canucks in exchange for Kellan Tochkin and a pick.