Kapanen was born in Vantaa, one of the tri-cities making up the capital area, while his father played in Helsinki. His first club was EVU Vantaa, but the bulk of his junior eligibility was spent with JoKP Joensuu and KalPa Kuopio while his dad had coaching assignments. KalPa gave him his first chance in the top league as an 18-year-old. His first season, 1990-91, coincided with the club's finest year ever, when they won a silver medal. Kapanen and his winning ways led to a fairytale career. During the same spring season, he also played for Finland's bronze medal team in the Under-18 European Junior Championship.
A two-time member of Finland's World Junior team (1992-1993), Kapanen's stature, if not his skills, was the reason for the reluctance of NHL observers to consider him for the draft. Four years later he could not be overlooked and the Hartford Whalers, now the Carolina Hurricanes, picked him in the fourth round of the 1995 NHL Entry Draft. In the fall he immediately joined the NHL club.
Unfortunately, his career almost came to an end even before it started. In his first training camp, he had a bad collision with defenceman Gerald Diduck. He lost his balance and while falling was hit by a knee. The result was a severe concussion and a lower back injury. Recuperating, his first season was split between the Springfield Falcons and Hartford. He played his first game two months after the incident. Scoring the tying goal late in the game for the Falcons while making his debut in the AHL boosted his confidence.
On December 13, 1995, Kapanen played in his first NHL game for the Whalers. A week later he got his first point, but it took until January 6th for him to get his first goal. On that day, he put the puck behind Craig Billington into the Boston Bruins' net. His second season was a step forward, if not offensively then at least in terms of adjusting to his new life and a new brand of hockey. The season also brought him the top plus-minus rating and the best scoring percentage on the team. In the third season he established himself has a bona fide NHL performer and has never looked back.
While Kapanen plays wing in the NHL, on the Finnish national team he plays center and is very often the driving force on his line. He has five medals from international tournaments. The most prestigious is the nation's first-ever IIHF World Championship gold medal in Sweden in 1995. The bronze from the Nagano Olympics in 1998, when Finland defeated Canada in the medal round, is a close second. He has another Olympic bronze from Lillehammer, Norway in 1994 and silvers from the 1994 World Championship in Italy and the 1998 World event in Switzerland. The latter is his last tournament to date as prior to the 1999 World Championship he twisted his knee and decided to pass on the 2000 event. He had given his all for the Hurricanes and was completely exhausted.
In 2001-02, Kapanen had a career year with the Hurricanes scoring 27 goals while adding 42 assists for 69 points as Carolina won the Eastern Conference title and qualified for their first Stanley Cup appearance only to come up short against a strong team from Detroit. Kapanen would also represent his country at the Winter Olympics for second time in 2002 at the Salt Lake City Games.
After a sub-par playoff, Kapanen was looking to rebound strong in the early going of the 2002-03 season. However, he would manage only six goals in 43 games with the Hurricanes, before he was traded to the Philadelphia Flyers. Upon his arrival with the Flyers, Kapanen registered 30 points (12-18-30) and was a key player in the team's run to the Eastern Conference Final. After falling to the eventual Stanley Cup champions from Tampa Bay in the Conference Final, Kapanen suited for yet again for his homeland at the 2004 World Cup of Hockey.
He competed in three more seasons with the Flyers, struggling to produce offensively in what would be his last season with the club. After 12 seasons with the Hartford Whalers, Carolina Hurricanes, and Philadelphia Flyers, Kapanen called it a career on June 3, 2008.