Wesley was drafted 3rd overall by the Boston Bruins in the 1987 NHL Entry Draft from the Portland Winter Hawks, appearing in 202 regular season games over 3+ seasons, scoring 49 goals and 175 assists for 224 points. Wesley began his NHL career with the Boston Bruins, whom he played for from 1987 to 1994. He earned a berth on the 1988 All-Rookie team. He reached the Stanley Cup Finals twice with the Bruins, in 1988 and 1990, though the Bruins lost both series to the Edmonton Oilers. As a rookie in the 1988 Finals, Wesley scored two goals in Game Four, a contest which would eventually be suspended due to power failure at Boston Garden. His dramatic last-minute goal in Game Five of the 1990 playoffs against Montreal would help the Bruins reach the Finals for the second time in three years. Prior to the start of the 1994-95 season, Wesley was traded to the Hartford Whalers for their first-round draft picks in 1995, 1996, and 1997. With the picks, the Bruins drafted Kyle McLaren, Johnathan Aitken and Sergei Samsonov, the latter of whom was Wesley's teammate in his final year in the NHL. Wesley moved with the Whalers to Carolina in 1997 and quickly became a leader. In 2002, he reached the Stanley Cup Finals for a third time. In March 2003, nearing the trade deadline, he was traded from Carolina to Toronto, joining the Maple Leafs for the rest of the 2002–2003 season in an effort for both teams to make the Stanley Cup playoffs. He re-signed with the Hurricanes at the end of the season. He got his fourth trip to the Stanley Cup Finals against the Edmonton Oilers. This would be Wesley's third time playing against the Oilers. Wesley won his first Stanley Cup on June 19, 2006 with the Hurricanes, defeating Edmonton in seven games, which is his childhood favorite team. When he won this, he ended one of the longest streaks for active players who had not yet won a Stanley Cup. Wesley played two more seasons with the Hurricanes before retiring, leaving him as the only player to have played in each of the Hurricanes' first 10 seasons since the team relocated to North Carolina. On June 5, 2008 Wesley announced his retirement after his 20th NHL season, and his 10th with the Carolina Hurricanes. He remains in the Hurricanes organization as Director of Defensemen Development. The Hurricanes retired Wesley's No. 2 jersey February 17, 2009, against the Boston Bruins, who Wesley began his NHL career with. Wesley was the only player to don #2 with the Hurricanes, as the number was previously retired by the Hartford Whalers in honor of Rick Ley. When the franchise relocated, Wesley changed his number from #20 to #2, marking the distinction of the number being retired by the same franchise for two different players in two different cities.