Stamkos was rated the top skater in North America by the NHL's chief scouting service. He led his minor league team with 105 points this year and he was also a member of the 2008 Canadian team that captured the World Junior Championships.
The centerman also fits a major need for Tampa Bay, which traded away Brad Richards to Dallas last season.
With the second choice in the draft, the Los Angeles Kings picked up defenseman Drew Doughty. He also played for Canada at the World Junior Championships.
Doughty was the first of four straight defenseman chosen in the first round. Zach Bogosian went to Atlanta, St. Louis chose Alex Pietrangelo and Toronto, which moved up to fifth from seventh in a trade with the New York Islanders, picked Luke Schenn.