Arnott, who signed a five-year contract with Nashville in July 2006, replaces defenceman Kimmo Timonen as captain. Timonen's rights were traded to Philadelphia in late June. General manager David Poile said they signed Arnott for his play.
"But we were also very interested in him for his leadership and experience. He has been one of the most consistent offensive contributors in the league over the last decade, has won the Stanley Cup and is a commanding and respected presence within our dressing room," Poile said.
Arnott, 32, tied for the team-high with 27 goals last season. He has 698 points in 892 career games with Edmonton, New Jersey, Dallas and now the Predators.
Dumont is coming off a career season with the Predators. He ranked second with 45 assists and 66 points, and he had four goals and six points in the playoffs in April. He was captain in Buffalo in January 2004.
Sullivan was an assistant captain last season and has averaged more than a point per game since being picked up by the Predators. He has 158 points in 150 games with Nashville, but he is recovering from back surgery and is expected to miss the first few weeks of the season.
Nashville's other captains were Tom Fitzgerald from 1998 through March 2002. He was replaced by Greg Johnson between 2002 and the end of the 2005-2006 season.
The Predators report for tests and physicals Thursday with their first practice Friday.