Cowen will receive $12.4 million over the four years, a source told ESPN.com's Pierre LeBrun.
Cowen began the 2012-13 season with the AHL's Binghamton Senators, getting three assists in three games. He had surgery in November to repair a torn labrum in his left hip, sidelining him until April when he made his NHL season debut against the Carolina Hurricanes.
The 22-year-old Cowen played seven regular-season NHL games last season, scoring one goal. He also played in each of Ottawa's 10 playoff games against the Montreal Canadiens and Pittsburgh Penguins, getting three assists and 21 penalty minutes.
Cowen was the Senators' first-round pick (ninth overall) in the 2009 draft.
He played in all 82 games of his rookie season with the Senators in 2011-12, scoring five goals and adding 12 assists.
Information from The Associated Press was used in this report.