Eller scored the biggest goal in the history of the Washington Capitals. The smooth-skating center's goal with 7:37 remaining in the third period in Game 5 of the 2018 Stanley Cup Final against the Vegas Golden Knights gave the Capitals a 4-3 win and clinched the first championship in Washington's 43 seasons in the NHL.

Eller is also among the trail blazers for the growing number of Danish players in the NHL.

He was the first player born, raised and trained in Denmark to be selected in the first round when he was chosen by the St. Louis Blues with the No. 13 pick in the 2007 NHL Draft. Since then, Mikkel Boedker (Arizona Coyotes, 2008), Nicklas Jensen (Vancouver Canucks, 2011) and Nikolaj Ehlers (Winnipeg Jets, 2014) have been selected in the first round.

Eller came up through the Danish program Rodovre, but at age 16 moved to Sweden to join Frolunda, where he played until the end of the 2008-09 season before signing an entry-level contract with the Blues. He spent most of the 2009-10 season with Peoria of the American Hockey League and was named to the AHL All-Rookie Team after finishing with 57 points (18 goals, 39 assists) in 70 games. He made his NHL debut on Nov. 5, 2009, scoring his first goal in a 2-1 loss to the Calgary Flames.

His tenure with the Blues ended after one season when he was traded to the Montreal Canadiens on June 17, 2010.

Eller played six seasons with Montreal, utilizing his strong skating ability, size and versatility while being deployed up and down the lineup, moving from wing to center and becoming a reliable penalty-killer. Eller also showed some offensive prowess, scoring 12 or more goals in four of his six seasons. On Jan. 4, 2012, Eller had his first NHL hat trick against the Jets, finishing with four goals and five points.

He helped fuel Montreal's run to the 2014 Eastern Conference Final with five goals and 13 points in 17 games.

The Canadiens traded Eller to the Washington Capitals on June 24, 2016 for two second-round draft picks. He had NHL career bests in goals (18) and points (38) with the Capitals in 2017-18.

Eller was one of the stars in Washington's run to the Cup in 2018. He scored the overtime goal that gave the Capitals their first win of the 2018 Stanley Cup Playoffs, in Game 3 of the Eastern Conference First Round against the Columbus Blue Jackets and had seven points (two goals, five assists) in the conference final against the Tampa Bay Lightning before his historic goal against Vegas gave the Capitals their first championship.

He scored 13 goals in 2018-19 and 16 in 2019-20, giving him seven consecutive seasons of at least 12 goals.

Eller was traded to the Colorado Avalanche by the Capitals on March 1, 2023, for a second-round pick in the 2025 NHL Draft. He signed a two-year contract with the Pittsburgh Penguins on July 1, 2023, an average annual value of $2.45 million, and was traded back to the Capitals by the Penguins on Nov. 12, 2024, for a third-round pick in the 2027 NHL Draft and a fifth-round pick in the 2025 NHL Draft.

Eller scored in his 1,000th NHL game, when the Penguins defeated the Canadiens 3-2 at PPG Paints Arena on Jan. 27, 2024. He became the first Denmark-born player to play 1,000 NHL games. He was also the ninth player to score at least one goal in the first and 1,000th game of his NHL career, joining Marian Gaborik, Milan Hejduk, Alex Kovalev, Evgeni Malkin, Joe Nieuwendyk, Gilbert Perreault, Jean Ratelle and Luc Robitaille.

Eller signed a one-year, $1.25 million contract with the Ottawa Senators on July 1, 2025. He was named to Team Denmark's roster for the Olympic Winter Games Milano Cortina 2026.