Sixers coach Brett Brown will oversee basketball operations on an interim basis.
Colangelo's wife, Barbara Bottini, admitted to establishing and operating the accounts, and an investigation by law firm Paul, Weiss, Rifkind, Wharton & Garrison LLP found forensic evidence to corroborate her admissions.
"Our investigation revealed substantial evidence that Mr. Colangelo was the source of sensitive, non-public, club-related information contained in certain posts to the Twitter accounts. We believe that Mr. Colangelo was careless and in some instances reckless in failing to properly safeguard sensitive, non-public, club-related information in communications with individuals outside the 76ers organization," according to the law firm, which was commissioned by the team to investigate the matter.
The move comes after a story by The Ringer brought to light the possibility that Colangelo had posted tweets from so-called burner accounts that were used to criticize current and former 76ers players.
Colangelo, a two-time NBA Executive of the Year, had discussed with ownership and upper management the possibility that his wife may have been involved in the posting of the tweets.
"I vigorously dispute the allegation that my conduct was in any way reckless" Colangelo said in a statement. "At no point did I ever purposefully or directly share any sensitive, non-public, club-related information with her.
"Her actions were a seriously misguided effort to publicly defend and support me, and while I recognize how inappropriate these actions were, she acted independently and without my knowledge or consent. Further, the content she shared was filled with inaccuracies and conjecture which in no way represent my own views or opinions. While this was obviously a mistake, we are a family and we will work through this together.
"Although I am not directly responsible for the actions, I regret this incident occurred and understand that it has become a distraction for the team. Therefore, the organization and I have mutually agreed to part ways."
The 76ers said in a statement it had "become clear Bryan's relationship with our team and his ability to lead the 76ers moving forward has been compromised" and that they had accepted his resignation.
Paul, Weiss, Rifkind, Wharton & Garrison LLP said Bottini deleted the contents of her iPhone with a factory reset of the device prior to surrendering it for forensic review, limiting the investigation.
Evidence found that Bottini established and operated four accounts -- Eric jr, Still Balling, Enoughunkownsources and HonestAbe -- but it seemed some of the information being posted was coming from Colangelo himself.
Some of the tweets took issue with All-Star center Joel Embiid's off-court behavior. Others claimed former center Nerlens Noel was a problem in the locker room and that Jahlil Okafor's injury issues may have scuttled a trade to the Pelicans.
The tweets included defenses of Colangelo's job performance and disparaging comments about his predecessor with the Sixers, Sam Hinkie, and his successor as president of the Toronto Raptors, Masai Ujiri. Other tweets alluded to sensitive information about events leading to Markelle Fultz's bizarre, season-long shooting problems.
NBA commissioner Adam Silver responded to the turmoil surrounding Colangelo and the Sixers at his annual NBA Finals news conference on May 31, cautioning against a rush to judgment on the controversy.
"The notion here was, let's find out what's going on," Silver said. "You have to separate sort of the chatter and sort of what either fans or, frankly, the media are saying, from the facts. And the first thing we have to do here is determine what the actual facts are in this circumstance."
It's a stunning fall for Colangelo, who was expected to lead the improving 76ers into an important summer when they are hoping to pursue LeBron James or another All-Star player to add to a young core that includes Embiid and Ben Simmons.
Instead that role will go to Brown, for now. The 76ers said the search for a new general manager would begin immediately.
"We find the situation to be disappointing for our entire organization," 76ers managing partner Josh Harris said. "We are determined to continue the tremendous progress we have made over the last two seasons in our quest to win an NBA championship."
Colangelo, the son of longtime sports executive Jerry Colangelo, was hired as president of basketball operations in 2016, after Hinkie abruptly resigned. Hinkie was the architect behind what has been called "The Process" -- the long-term tearing down and rebuilding of the Sixers.
Bryan Colangelo previously served as Raptors general manager, adding the 2007 Executive of the Year award to the one he won two years earlier in Phoenix. But he lost his job there after Toronto missed the playoffs for the fifth consecutive season, and Ujiri took over basketball operations.
Information from ESPN'sAdrian Wojnarowski andZach Lowe and The Associated Press was used in this report.
Kellerman: Colangelo had to go
Max Kellerman says if the 76ers want any chance to land LeBron James this offseason, Bryan Colangelo could not be involved.