The 32-year-old has 63 points last season, the eighth straight year the Montrealer has recorded 50 or more points.
Ribeiro is going into the final year of a five-year contract and will be paid $5 million next season.
Ribeiro spent six season with the Stars and tallied a career-high 83 points (27 goals, 56 assists) during the 2007-08 season. He added 17 points (three goals, 14 assists) in 18 playoff games that year.
Eakin is coming off a rookie campaign in Washington where he collecting four goals and four assists in 30 games.
Stay Connected
NHL.TV™
NHL GameCenter LIVE™ is now NHL.TV™.
Watch out-of-market games and replays with an all new redesigned media player, mobile and connected device apps.
Introducing the new official NHL App, available for iPhone, iPad and Android smartphones and tablets. A host of new features and improved functionality are available across all platforms, including a redesigned league-wide scoreboard, expanded news coverage, searchable video highlights, individual team experiences* and more. The new NHL App on your tablet also introduces new offerings such as 60fps video, Multitasking** and Picture-in-Picture.
*Available only for smartphones
** Available only for suported iPads