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.