Angelo was under contract through 2013, but the team decided change is needed after finishing 8-8, the fourth time in five seasons the franchise has not reached the playoffs.
His dismissal comes less than a year after the Bears hosted the 2010 NFC Championship Game.
Chicago won three division titles and reached Super Bowl XLI -- in which the Bears fell to Indianapolis to end the 2006 season -- under Angelo, who joined the team prior to the 2001 campaign.
Martz was hired by Chicago in February of 2010, taking over for Ron Turner. He led the offense to 334 points, an 11-5 record and NFC North title last season, but in 2011, the Bears regressed despite scoring 353 points.
The 60-year-old made his mark as the offensive whiz behind the "Greatest Show on Turf" in St. Louis under Dick Vermeil, then became head coach prior to the 2000 season. Since being let go by the Rams, Martz had been offensive coordinator for Detroit (2006-07) and San Francisco (2008).
Also on the chopping block was quarterbacks coach Shane Day.
Day had to contend with an inconsistent Jay Cutler, and once Cutler was out for the latter half of the season with a broken thumb, tried to turn things around with Caleb Hanie -- who ended the year with three TDs and nine interceptions.
"After meeting with Mike this afternoon, we both felt it was best to move in different directions," Chicago head coach Lovie Smith said. "I appreciate the job he and Shane did for us over the last two years."