Hagman was drafted by the Panthers in the 3rd round, seventieth overall in the 1999 NHL Entry Draft. After 3 seasons in his native Finland, Hagman joined the Wikipedia:Florida Panthers roster in the 2001–02 NHL season. By the end of the 2003–04 NHL season, Hagman had played 233 games for the Panthers, scoring 28 goals and 46 assists for 74 points and 50 penalty minutes. During the 2004–05 NHL lockout, which cancelled the 2004–05 NHL season, Hagman played for Swiss outfit Davos. After previously clearing waivers, he was traded to the Dallas Stars in return for a seventh round draft pick. Hagman's father, Matti, was the first Finnish player to play in the NHL, and accordingly they are the first Finnish father and son to have played in the league. Hagman won a silver medal at the 2006 Winter Olympics in Torino, Italy with team Finland.
Hagman recorded his first career NHL hat-trick on February 28, 2008 in a 7-4 victory against the Chicago Blackhawks.
On July 1, 2008 the Toronto Maple Leafs signed Hagman to a 4 year deal worth $3 million a season. Hagman has produced well in his time with the Maple Leafs, combining with fellow newcomers Mikhail Grabovski and Nikolai Kulemin to form a offensively dynamic scoring line. The trio's skill and speed has proved to be a catalyst for any success the young Maple Leaf team have experienced in the 2008-09 season.