It is understood Judge Jeff Blackett's conclusion called for Thomas's resignation along with nine non-executives on the management board.
He will remain acting chief executive until a permanent appointment is made.
The rest of the management board have survived after a vote of no confidence was reported to have been defeated by a majority verdict.
In a statement released by the RFU, Thomas said: "This was a difficult day for the Union but at the end of the day this does now mean we can finally move on.
"The most important thing was that we maintained stability for staff and our other partners and in the coming weeks I will be ensuring that we navigate to calmer waters and that we can get on with our core purpose of rugby."
The RFU council discussed the 52-page report's findings in a four-hour meeting on Sunday.
The full report will not be made public, but an executive summary will be put together by the panel in "a timely fashion".
Thomas, who was made RFU chairman in April 2005, will remain chairman of Rugby World Cup 2015 - which is being staged in England and Wales - and will stay as an RFU representative on the International Rugby Board.
His decision to stand down leaves the RFU without a permanent chairman or permanent chief executive.
Blackett said he was pleased the report was received in "the spirit it was delivered".
"As guardians of the game [the] council had some important decisions to take and discussions were robust and emotive in that regard," he commented.
A TROUBLED YEAR AT THE RFU
- John Steele appointed chief executive, tasked with undertaking a "comprehensive review" of the RFU
- Steele's shake-up plans are approved by the management board, leading to creation of three key roles: operations director, development director and elite performance director, a position rumoured to be tailor-made for Sir Clive Woodward
- Performance director responsibilities are downgraded so as to no longer include the management of the senior England squad
- Decision to change performance director role is reversed by management board, prompting "clear-the-air" talks between Steele and RFU chairman Martyn Thomas
- Woodward formally withdraws from performance director recruitment process
- Steele resigns following emergency board meeting
- RFU disciplinary officer Judge Jeff Blackett begins wide-ranging inquiry
- Rejigged RFU management structure confirms Thomas will stay on as acting chief executive, with Peter Baines as board chairman
- Thomas stands down as chairman of RFU following release of Blackett's report
"I would like to thank my panel for a job well done and hope that as a game we can now draw a line under the events of the past few months and get on with rugby."
Oxfordshire RFU council member Paul Murphy will serve as interim chairman pending a special general meeting, when Thomas's permanent replacement will be decided.
That meeting, however, can not take place for at least 60 days, meaning the RFU will be without a chairman when the World Cup in New Zealand starts in less than nine weeks.
The standing down also raises the possibility of potential embarrassment for the RFU if no fixed chairman is in place when the World Cup is handed over to England as the host nation for 2015.
Murphy told BBC Radio 5 live that could be the case, but added that it was more important to appoint the right people to the jobs.
"We do have, I'd like to think, competent people standing in those roles at the moment," he said.
"In a lot of cases it's about getting the job done correctly and right. There's no need to rush things through."
Meanwhile, the search continues for an elite performance director, the handling of which was said to have been a key factor in the board's loss of confidence over Steele's position as chief executive.
Blackett's wide-ranging investigation reviewed the RFU's hiring procedures.
The review panel also comprised RFU council members Geraint Ashton-Jones and Malcolm Wharton, plus Andy Reed, chairman-elect of the Sport and Recreation Alliance, and Vic Luck, formerly general manager of IBM UK.
The panel interviewed more than 65 key figures, reviewed over 90 media articles and took on board the conclusions of an earlier review of the performance director recruitment process, conducted by RFU chairman of governance Peter Baines.
The report focused on the process of Steele's appointment in June 2010, as well as the circumstances leading to his departure after an emergency meeting last month.
The process of trying to fill the performance director role was also scrutinised in Blackett's investigation.
Steele resigned from the RFU last month
The job had seemingly been set up for 2003 World Cup-winning coach Sir Clive Woodward, only for the 55-year-old to formally pull out of the process following changes in the specification of the role.
Steele's removal from the job description of overall responsibility for the senior England team seemed to block the possibility of Woodward's return.
Shortly afterwards the RFU board reverted back to the original description but Woodward withdrew, stating his commitment to his post as director of sport with the British Olympic Association.
However, despite it featuring heavily in the report, Murphy insisted Thomas's stepping down was "not directly" related to the handling of the performance director position.
"We addressed a governance issue which was where Martyn was wearing two hats which everyone felt a bit uncomfortable about in terms of him being the interim chief executive as well as chairman of the board," added Murphy.
"He quite rightly helped us resolve it. He got a very good endorsement in terms of him carrying on in his role as acting chief executive.
"We must now start moving forward. It is a difficult time for the Union, there's been some issues about the reputation in the press.
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