The 29-year-old forward scored 13 points (four goals, nine assists) in 53 games with the Buffalo Sabres last season.
"We're excited to add an experienced veteran like Riley to our organization," Kraken general manager Ron Francis said. "His versatility, strong penalty-killing ability and skill in the face-off circle make him a valuable addition to our forward group."
Sheahan won 50.9 percent of his Sabres-high 503 face-offs last season. In 10 NHL seasons he has won 50.3 percent of his face-offs, including 51.0 percent at even strength.
Selected by the Detroit Red Wings with the No. 21 pick in the 2010 NHL Draft, Sheahan has scored 177 points (70 goals, 107 assists) in 566 games with the Red Wings, Pittsburgh Penguins, Florida Panthers, Edmonton Oilers and Sabres, and seven points (three goals, four assists) in 33 Stanley Cup Playoff games.