Grönman was drafted in the second round of the 1992 NHL Entry Draft by the Quebec Nordiques. After spending 4 years in Finland developing his skills, the Nordiques still owned his negotiating rights but Gronman was not offered a professional contract. Soon after, the Quebec franchise moved to Colorado, becoming the Avalanche; Gronman's NHL negotiating rights were traded to the Chicago Blackhawks by the Colorado Avalanche on July 10, 1996, in exchange for the Chicago Blackhawks' second-round pick in the 1998 NHL Entry Draft. Colorado selected Phillippe Sauve with that pick.
A little more than a year later on October 27, 1997, the Blackhawks traded Gronman to the Pittsburgh Penguins in exchange for veteran forward Greg Johnson. On October 18, 1998, while playing in a game for Pittsburgh's farm team, the Kansas City Blades of the IHL, Gronman suffered a significant knee injury causing him to miss the majority of the 1998-1999 IHL season. Soon after Gronman's contract expired, and with no NHL or minor league interest his professional North American career was over. He returned overseas and played for TPS, Lukko and Jokerit. Gronman would also help Finland win a bronze medal at the 1998 Winter Olympics.
