Eller, a native of Denmark, was drafted 13th overall in the 2007 NHL draft by the St. Louis Blues, who he played for during his first seven NHL games. He was then traded to Montreal where he carved out the start of his career as a consistent player for the Canadiens for six years. He then moved to Washington in 2016 where he would realize the most success of his career where he won a Stanley Cup in 2018. After seven years in Washington, Eller moved to Colorado where he only played 24 games. Then in the 2023 offseason, Eller signed with the Penguins and has been there to this day.