A report into the controversial sacking of then chief executive John Steele in June 2011 criticised Thomas and accused him of leaking information.
Thomas, who was acting chief executive at the time the report was issued to RFU member clubs, denied the claims and was considering legal action.
The apology comes after a further independent review.
An RFU statement issued on Monday read: "Following the departure of John Steele on 9th June 2011, the RFU Council set up a review to examine the events that led to his departure and further to consider how and why confidential information was leaked to the media and to see what lessons could be learned.
"The Review Panel conducted interviews with more than 20 individuals, received written evidence from in excess of 40 people and reviewed numerous documents. The Panel submitted its report to the RFU Council on 8th July for debate on 10th July.
"The Panel's report was debated again on 3rd September 2011. At this later meeting, a decision was taken to publish the report. It was sent to member clubs and there was some further onward publication.
"The report made a number of conclusions. Amongst these it concluded that Martyn Thomas, the then Chairman and Acting Chief Executive:
(i) had inadvertently, but improperly and repeatedly passed confidential information in relation to the RFU either directly or indirectly through third parties to members of the media;
(ii) had inappropriate contact with one of the candidates for the role of RFU Performance Director and breached confidentiality between prospective job applicants.
"The RFU now accepts that there was insufficient evidence to support these conclusions. Consequently, the RFU believes it right that these conclusions be withdrawn.
"The RFU therefore apologises to Martyn Thomas.
"The RFU is now pleased to bring this matter to a close. We wish to thank Mr Thomas for his many positive achievements during his long and valued service to the Union and wish him well for the future.
"It is further agreed that neither Mr Thomas nor the RFU will comment further on this matter."
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