The club made the announcement on Thursday, ahead of its season opener against the Carolina Hurricanes.
Lee takes over from John Tavares, who took on the captaincy in 2013 and served in the role until he departed for Toronto in free agency on July 1.
Lee, 28, put together a career-best season in 2017-18 with 40 goals and 62 points through 82 games. The Minnesota native has spent his entire career so far in New York, registering 124 goals and 207 points in 343 games since being drafted in the sixth round (No. 151 overall) in 2009.