Originally from Denmark, Eller was drafted 13th overall in the 2007 NHL Draft by the St. Louis Blues, where he played his first seven NHL games. He was then traded to Montreal, where he spent six years establishing himself as a consistent player for the Canadiens. In 2016, he moved to Washington, where he achieved the highlight of his career by winning a Stanley Cup in 2018. After seven years with the Capitals, Eller played 24 games for Colorado before signing with the Penguins in the 2023 offseason.