The deal is worth $2.65 million, with 2012-13 worth $1.15 million and '13-14 good for $1.5 million, a source told ESPN.com's Pierre LeBrun.
The 23-year-old Eller had 16 goals and 12 assists in 79 games last season. He has 25 goals and 22 assists in 163 career games in three seasons with St. Louis and Montreal.
He joined the Canadiens in the June 2010 trade that sent goalie Jaroslav Halak to St. Louis.
Information from The Associated Press was used in this report.