In 1997, Varis moved to North America, where he played a season with the Indianapolis Ice in the IHL, as well as a single NHL game with the Chicago Blackhawks. He has also played in the German ice hockey league and the Swiss first and second leagues.
Varis has also represented Finland in international play.
Varis scored 268 goals in SM-Liiga. He also scored 7 goals in 7 games in European Cup.
| Regular season | Playoffs | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Season | Team | League | GP | G | A | Pts | PIM | GP | G | A | Pts | PIM | ||
| 1987–88 | Karhu-kissat | Finnish 1st div. | 42 | 9 | 15 | 24 | 21 | -- | -- | -- | -- | -- | ||
| 1988–89 | Karhu-kissat | Finnish 1st div. | 44 | 18 | 19 | 37 | 26 | -- | -- | -- | -- | -- | ||
| 1989–90 | Karhu-kissat | Finnish 1st div. | 42 | 30 | 24 | 54 | 44 | -- | -- | -- | -- | -- | ||
| 1990–91 | Kookoo | Finnish 1st div. | 44 | 20 | 31 | 51 | 42 | -- | -- | -- | -- | -- | ||
| 1991–92 | Ässät | SM-liiga | 36 | 13 | 23 | 36 | 24 | 8 | 2 | 2 | 4 | 6 | ||
| 1992–93 | Ässät | SM-liiga | 46 | 14 | 35 | 49 | 42 | 8 | 2 | 2 | 4 | 12 | ||
| 1993–94 | Jokerit | SM-liiga | 31 | 14 | 15 | 29 | 16 | 11http://www.nettby.no/ | 3 | 4 | 7 | 6 | ||
| 1994–95 | Jokerit | SM-liiga | 47 | 21 | 20 | 41 | 53 | 11 | 7 | 2 | 9 | 10 | ||
| 1994–95 | Haukat | Finnish 1st div. | 1 | 0http://www.nettby.no/ | 1 | 1 | 2 | -- | -- | -- | -- | -- | ||
| 1995–96 | Jokerit | SM-liiga | 50 | 28 | 28 | 56 | 22 | 11 | 12 | 7 | 19 | 6 | ||
| 1996–97 | Jokerit | SM-liiga | 50 | 36 | 23 | 59 | 38 | 9 | 7 | 4 | 11 | 14 | ||
| 1997–98 | Chicago Blackhawks | NHL | 1 | 0 | 0 | 0 | 0 | -- | -- | -- | -- | -- | ||
| 1997–98 | Indianapolis Ice | IHL | 77 | 18 | 54 | 72 | 32 | 5 | 3 | 4 | 7 | 4 | ||
| 1998–99 | Kölner Haie | DEL | 52 | 10 | 25 | 35 | 22 | 5 | 3 | 0 | 3 | 4 | ||
| 1999–00 | Jokerit | SM-liiga | 53 | 21 | 25 | 46 | 44 | 10 | 0 | 5 | 5 | 14 | ||
| 2000–01 | Jokerit | SM-liiga | 56 | 27 | 43 | 70 | 38 | 5 | 0 | 2 | 2 | 4 | ||
| 2001–02 | Jokerit | SM-liiga | 6 | 2 | 0 | 2 | 0 | -- | -- | -- | -- | -- | ||
| 2001–02 | ZSC Lions | Swiss | 10 | 2 | 2 | 4 | 6 | 10 | 3 | 1 | 4 | 4 | ||
| 2001–02 | GCK Lions | Swiss-B | 16 | 6 | 15 | 21 | 29 | 2 | 0 | 0 | 0 | 8 | ||
| 2002–03 | GCK Lions | Swiss-B | 28 | 16 | 21 | 37 | 16 | 4 | 1 | 0 | 1 | 2 | ||
| 2003–04 | Tappara | SM-liiga | 55 | 9 | 19 | 28 | 38 | 3 | 1 | 1 | 2 | 0 | ||
| 2004–05 | Jokerit | SM-liiga | 56 | 13 | 17 | 30 | 28 | 12 | 3 | 4 | 7 | 10 | ||
| 2005–06 | Jokerit | SM-liiga | 56 | 18 | 13 | 31 | 56 | -- | -- | -- | -- | -- | ||
| 2006–07 | Jokerit | SM-liiga | 54 | 17 | 28 | 45 | 56 | |||||||
| NHL totals | 1 | 0 | 0 | 0 | 0 | -- | -- | -- | -- | -- | ||||
| SM-liiga totals | 596 | 233 | 289 | 522 | 455 | 88 | 37 | 33 | 70 | 82 | ||||