Steele left the RFU after less than a year in his role as attempts to recruit a new performance director became clouded in controversy.
Blackett's review has not been made public but it is understood to have called for the removal of Thomas and nine non-executive members of the RFU Board.
The rest of the management board survived a vote of no confidence at a four-hour RFU meeting on Sunday afternoon but Thomas tendered his resignation less than a week after he was made acting chief executive.
"This was a difficult day for the Union but at the end of the day this does now mean we can finally move on," said Thomas, who will remain CEO until a permanent replacement for Steele can be found.
"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."
Thomas, who has long been the public face of the RFU Board, has been chairman of England's governing body since 2005.
He will continue in his role as chairman of Rugby World Cup 2015 and will stay as an RFU representative on the International Rugby Board.
But while Thomas' decision to step aside appears heavily linked to Blackett's review, the RFU's acting chairman Paul Murphy insists it was not the primary factor in the decision.
"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," Murphy told BBC Radio 5 Live.
"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. We need to start repairing these things."