Moulson grew up in Mississauga, Ontario, playing minor hockey for A Erindale, AA York Toros, AAA North York Canadiens, AAA Mississauga Senators, AAA Markham Islanders, AAA Mississauga Reps and at Midget for the AA Mississauga Braves of the Greater Toronto Hockey League. He also attended Our Lady of Mount Carmel Secondary School in Mississauga, where he was a part of the school's hockey team. After his midget career, Moulson signed with the Guelph Dominators Junior B club of the Midwestern Ontario Junior B League for the 2000–01 and 2001–02 seasons. In the following four years, Moulson attended Cornell University to play for the Big Red ice hockey team of the ECAC Hockey conference. Whilst playing for Cornell, Moulson was drafted 263rd overall by the Pittsburgh Penguins in the 2003 NHL Entry Draft. In 2006, he graduated from Cornell, where he served as team captain of the hockey team and was a member of the Quill and Dagger society in his senior year.
Professional
Moulson signed with the Los Angeles Kings as a free agent on an entry-level contract on September 1, 2006. He was then assigned to the Kings' minor league affiliate, the Manchester Monarchs of the American Hockey League, for the 2006–07 season, where he registered 57 points in 77 games. He made his NHL debut in the 2007–08 season on November 2, 2007, against the San Jose Sharks. Moulson also scored his first career NHL goal in the 5–2 Kings victory. On July 6, 2009, Moulson signed a one-year contract with the New York Islanders. He was a leading scorer in the NHL pre-season and made the team out of camp as a linemate of John Tavares. He scored his first NHL hat-trick — a natural hat trick — on December 3, 2009, against the Atlanta Thrashers. On July 27, 2010, Moulson signed a one-year, $2.45 million contract extension with the Islanders just minutes before his arbitration hearing was scheduled to begin. On January 27, 2011, he then signed a three-year, $9.45 million contract extension with New York. After the 2011–12 season, Moulson became the first New York Islander since Žigmund Pálffy to post three consecutive 30-goal seasons. On May 16, 2013, Moulson was named a finalist, along with Patrick Kane and Martin St. Louis, for the Lady Byng Memorial Trophy, awarded annually to the player adjudged to have exhibited the best type of sportsmanship and gentlemanly conduct combined with a high standard of playing ability. On October 27, 2013, Moulson and a 2015 first- and second-round draft pick were traded by the Islanders to the Buffalo Sabres in exchange for Thomas Vanek. Moulson scored two goals in his first game as a Sabre in a 4–3 losing effort to the Dallas Stars. Moulson and Sabres forward Cody McCormick were then both traded to the Minnesota Wild on March 5, 2014, in exchange for Torrey Mitchell, a 2014 second-round pick and Minnesota's 2016 second-round pick. On July 1, 2014, Moulson returned to the Sabres, signing a five-year, $25 million contract. After a difficult 2015–16 season that saw Moulson struggle under new Sabres coach Dan Bylsma and score a career-low 21 points, he was rumored to be a buyout candidate. The Sabres ultimately decided to keep Moulson, and he eventually improved to 32 points in 2016–17. Moulson was placed on waivers by the Sabres on December 4, 2017. He cleared waivers the following day and, with the Sabres unwilling to clear a roster spot on the Rochester Americans for him at the expense of their up-and-coming prospects, was lent to the Ontario Reign. On July 24, 2019, Moulson signed a one-year contract with the Hershey Bears. He was recently selected as captain of the 2020 AHL All-Star Classic alongside Matthew Ford.