It was the latest in a flurry of trades by the Rangers, who received backup goaltender Jamie McLennan, center Blair Betts and minor league right wing Greg Moore from Calgary and also sent the Flames a seventh-round pick in 2004.
Simon, 32, had 14 goals, nine assists and an impressive plus-minus rating of plus-14 in 65 games for the Rangers this season.
But 6-3, 232-pound Simon is known best as one of the NHL's most feared fighters. He is second in the league with 225 penalty minutes. His value went up recently as he scored five goals in six games.
"We have been interested in Chris for some time," Flames general manager and coach Darryl Sutter said. "He is a big strong player who will also provide us with an offensive contribution and is having a good season."
A 12-year veteran, Simon signed a one-year contract with the Rangers in July. He has 122 goals, 258 points and 1,571 penalty minutes in 592 games.
Trying to make the playoffs for the first time since 1996-97, the Flames are the seventh seed in the Western Conference with 74 points, one ahead of Los Angeles and five in front of St. Louis.
The Rangers likely will miss the playoffs for the seventh straight year, prompting president and general manager Glen Sather to clean house.
McLennan, 32, who is eligible to become an unrestricted free agent in July, served as Calgary's backup goalie and will play the same role for the Rangers. He was 12-9-3 with a 2.20 goals-against average and .910 save percentage for the Flames.
With McLennan gone, Calgary probably will keep goaltender Roman Turek, who cleared waivers Saturday. Calgary hoped a team would
pick him up, but Turek is due to make $5 million next season.
Betts, 24, has been sidelined since undergoing shoulder surgery two months ago. He had one goal and two assists in 20 games this season.
Moore, 19, was a fifth-round pick of the Flames in last year's draft.
The Rangers also claimed forward Josh Green off waivers from the Flames. Green had two goals and four assists in 36 games with Calgary this season. He played four games with New York last season before being waived.
Information from SportsTicker and The Associated Press was used in this report.