Strålman was selected in the seventh round, 216th overall, by the Toronto Maple Leafs in the 2005 NHL Entry Draft.
Earlier in the same year, on April 4, Anton had signed a two year deal with Timrå IK. During the following 2005-06 season, Strålman adapted to Elitserien quickly and became a regular. On January 20, 2006, this effort was recognized as he was named the third in the line of four candidates for Elitserien Rookie Of The Year for 2006. The award was eventually won by the forward Nicklas Bäckström.
On May 16, 2007, it was announced that Strålman had signed a three year contract with the Maple Leafs. He made his North American professional debut on October 6, 2007 with the Toronto Marlies and played his first game for the Maple Leafs on October 23, in a home game against the Atlanta Thrashers. On March 21, 2008, he scored his first NHL goal in a game against the Buffalo Sabres and recorded his first multi-goal game against the Montreal Canadiens on March 29.