Drouin, who asked to be traded then was demoted and suspended by the Lightning during last season, scored in each of his two regular-season games after he was recalled from Syracuse of the American Hockey League, and had 14 points (five goals, nine assists) in 17 Stanley Cup Playoff games.
The 21-year-old did not get to play with Stamkos until Game 7 of the Eastern Conference Final against the Pittsburgh Penguins because the Lightning captain was recovering from surgery to treat a blood clot.
Stamkos, 26, chose to stay with the Lightning before entering free agency, signing an eight-year contract reportedly worth $68 million on June 29. Defenseman Victor Hedman, 25, agreed to an eight-year contract extension worth $63 million two days later.
"Victor and I are extremely close friends," Stamkos told reporter Pierre LeBrun. "We came up in this organization as 18-year-old kids. To say that we're going to be together for the long run, and on one team, that's something special.
"We have talked a lot throughout this process. I joke with him that sometimes I forget the time difference (with Sweden) and I'm calling him at 4 in the morning. But he's always getting back to me as quick as he can. It was extremely exciting to see him sign. A big reason why both of us stuck around is because of the relationship that we have as teammates and as friends as well."