Oduya becomes the sixth player from the 2014-15 Stanley Cup-winning team to leave the organization.
Oduya, 33, won two Stanley Cups during the last three and half seasons with the Blackhawks. He had nine goals and 34 assists and averaged 20:37 of ice time in 219 regular-season games for the Hawks. The defenseman signed a $10.125 million contract extension following the 2011-12 season.
The 6-foot 188-pound defenseman was acquired by the Hawks in a trade with the Winnipeg Jets for a second- and third-round pick in the 2013 draft.
David Rundblad, who both signed two-year extensions, will likely fill Oduya's spot. Rundblad recorded three goals and 14 points in 49 this past season. He averaged less than 13 minutes of ice time per game, a number that will rise in his new role on the blue line. Van Riemsdyk had one assist in 18 regular season and four playoff games.
The Stockholm, Sweden native has 31 goal and 121 assists in 664 career NHL games across parts of 11 seasons with the New Jersey Devils, Atlanta Thrashers, Jets and Hawks. He was originally drafted in the seventh round, 221st overall, in the 2001 NHL draft by the Washington Capitals.