They'll be joined in the class of 2013 by Geraldine Heaney, the third woman to be enshrined in the hall, and coach Fred Shero, who led the Philadelphia Flyers to the Stanley Cup in 1974 and '75. He was selected posthumously in the builder category.
"There's no sense looking back as to why it didn't happen sooner, because today's a happy day to celebrate the fact that a guy that deserves it immensely has finally been elected to the Hall of Fame," Flyers chairman Ed Snider said.
Chelios and Niedermayer earned hockey's biggest individual honor in their first year of eligibility.
Shanahan was a teammate of Chelios' in Detroit, and played with Niedermayer during the Olympics in 2002 when Canada won gold.
"When you got to play with them, it was a thrill," Shanahan said. "I spent some years playing with Cheli, and there's not another guy that you would want to go into a tough situation looking out for you.
"It absolutely makes it more special to go in with people I not only played against, but played with and got to know well."
The induction ceremony is scheduled for November.
Niedermayer won four Stanley Cups in 17 full NHL seasons to go along with a Norris Trophy and Conn Smythe Trophy. He played for the New Jersey Devils from 1991-92 through the 2003-04 season and finished his career in Anaheim in 2010.
Chelios played 23 full seasons and parts of three more, taking part in his final NHL game at age 48.
"I was part of an era, Chris was part of a few," Niedermayer joked.
Among the game's best U.S.-born players, Chelios won the Norris Trophy as the league's top defenseman three times. The Chicagoan split much of his career with three storied franchises in Montreal, Chicago and Detroit and was asked which team he will be affiliated when he is inducted into the Hockey Hall of Fame.
"U.S.A.," he said.
Shanahan finished his career with 656 goals and 698 assists. He won three Stanley Cups with the Red Wings, an Olympic gold medal and was the quintessential scoring power winger of his era. Shanahan started his career with the Devils, went on to play in St. Louis, Hartford, Detroit and for the New York Rangers before ending his playing career back in New Jersey.
Heaney was a defenseman on Canada's gold-medal-winning team at the 2002 Olympics and is considered one of the best female players in history.
"As a young girl playing hockey, never in my wildest dreams did I think I would be going into the hall," she said.