Callahan fills the vacancy left by former captain Chris Drury, who was bought out by the Rangers earlier this summer and subsequently retired.
"Obviously it's a privilege and an honor," said Callahan, who served as an alternate captain the previous two seasons. "The way I'm going to approach it is going to be the same as wearing an A. The things I do on the ice and off the ice -- there's a reason why I feel I got the A -- and I'm continuing on now with the C."
Coach John Tortorella said Callahan was an easy choice.
"He has the respect of his teammates, the respect of his coaches and the respect of the organization," Tortorella said. "He does it the right way on the ice, he does it the right way off the ice and he's matured into this."
Selected by the Rangers in the fourth round of the 2004 draft, Callahan has evolved into a player that embodies the identity the team is trying to create.
"We're a straight-ahead team, a hard-working hockey club, no nonsense," Tortorella said. "It's a good time for a Ryan Callahan-type player to be the captain of this club."
Callahan, who signed a three-year, $12.825 million deal with the team in July, is coming off a career-best season of 23 goals and 25 assists.
When Tortorella told him the news Friday, he advised Callahan not to change a thing.
"I have to continue to do what I do and not let a letter on my sweater affect my game or how I approach a game," Callahan said.
With young players Callahan and Staal comprising the majority of the team's leadership structure, the organization wanted to add 31-year-old Richards' veteran experience to the group.
"I think Brad is going to add a tremendous amount to our leadership group," said Tortorella, who coached Richards in Tampa. "I think it's a good fit."
The highly coveted center, who signed a nine-year, $60 million deal with the Rangers this offseason, said he'd assume that level of responsibility regardless of whether he was officially given an 'A.'
"That role was going to be on me," Richards said. "I signed a nine-year contract, [played] 12 years in the league, so that role was going to be on me no matter what."
Richards said hasn't spent too much time with Callahan, but from what little he has seen, it's obvious the type of respect Callahan commands from his teammates.
"There's going to be no issue there, I can tell that," Richards said. "He's a great person, teammate, and you call tell all the guys really like him."
Katie Strang covers the NHL for ESPNNewYork.com.