Peverley was born in Kingston, Ontario but moved to Guelph, Ontario at age eight, playing most of his minor hockey for the Guelph Reps of the OMHASouth Central AAA League. In his Midget year, he played one season with the Toronto Young Nats of the MTHL before moving back to his home area to play for the Kitchener Dutchmen Jr.B. club of the OHA Midwestern league. After his Jr.B. season with the Dutchmen, Peverley was selected by Don Cherry and the Mississauga IceDogs in the sixth round, 124th overall, of the 1999 OHL Draft. Peverley chose to maintain his NCAA eligibility, however, and instead signed for the 1999–2000 season with the Milton Merchants of the OHA's Provincial Jr.A. League. He later accepted an NCAA scholarship at the end of the season. Prior to beginning his professional career, Peverley played collegiate hockey for the St. Lawrence University Skating Saints, where he led the Skating Saints in points in three of his four seasons. Undrafted, Peverley made his professional debut in the 2004–05 season in the ECHL with the South Carolina Stingrays before playing a solitary game with the Portland Pirates in the American Hockey League. After leading the Milwaukee Admirals in points midway in the 2006–07 season, his second season with the team, Peverley was signed by the team's parent club, the Nashville Predators, on January 17, 2007, appearing in 13 NHL games by season's end. Peverley split the 2007–08 season with the Predators and the Admirals, appearing in all six games for the Predators in the Stanley Cup playoffs against the eventual Stanley Cup-winning champions, the Detroit Red Wings. On January 10, 2009, Peverley was claimed off waivers by the Atlanta Thrashers after accumulating nine points in 27 games. The switch to Atlanta rejuvenated his career, as he collected 35 points in 39 games for the remainder of the 2008–09 season and earned a two-year, $2.6 million contract with the Thrashers in the process. On February 18, 2011, Peverley was traded by the Thrashers, along with Boris Valábik, to the Boston Bruins in exchange for Blake Wheeler and Mark Stuart. He won the Stanley Cup with the Bruins on June 15, 2011. As a result of the 2012–13 NHL lock-out, Peverley signed a contract with JYP of the FinnishSM-liiga. On July 4, 2013, Peverley was traded, along with Tyler Seguin and Ryan Button, to the Dallas Stars in exchange for Loui Eriksson, Joe Morrow, Reilly Smith and Matt Fraser.
In-game cardiac incident
In September 2013, before the start of the Stars' 2013 training camp, Peverley underwent a surgical procedure to help with an irregular heartbeat. Six months later, Peverley collapsed on the team bench during a game against the Columbus Blue Jackets, due to the cardiac issue. Subsequent surgery corrected the irregular heartbeat, and Peverley spent the 2014–2015 season as a volunteer assistant coach for the Stars' AHL affiliate, the Texas Stars. He formally announced his retirement in September 2015, remaining with the Stars in the front office as the team's Player Development Coordinator.
International play
Peverley made his international debut in 2010, when he was named to the Canadian national team for the 2010 World Championship. He played all seven games for Canada, who finished seventh, and had one goal and three assists; his one goal was scored in a game against Norway.
