The deal carries an average annual value of $4.975 million.
"Drake represents an integral component of our future at forward," said Senators general manager Pierre Dorion in a press release.
"Dating to his first pro season, he has steadily progressed to the point where he is now widely recognized as a bonafide top-line NHL winger. He possesses a strong ability to play at both ends of the ice, is a key power-play contributor and someone we expect to be a prominent player for us for several years to come."
The 23-year-old ranked fourth in scoring and tied for second in goals on the Senators last season with 17 markers and 34 points in 56 games.