Eller, 23, earned the deal after notching 16 goals and 12 assists for 28 points with the Habs last season. He has spent two seasons in Montreal, posting 45 points in that span.
The St. Louis Blues selected the Rodovre, Denmark native 13th overall in the 2007 draft. But he only played seven games with the Blues before joining the American Hockey League's Peoria Rivermen.
Eller joined the Canadiens in June 2010, after he and Ian Schultz were traded for goalie Jaroslav Halak.