And they blasted relentless attacks on him as "absurd" and "disgraceful".
The Ibrox director has come under huge pressure from supporters in recent weeks as tensions have once again escalated between the terraces and the boardroom. Police Scotland have launched a probe into comments made by Wallace at Rangers' agm last December while revelations about his remuneration package - which includes a 100% bonus - and 120-day business review have infuriated fans in the midst of another cash crisis at Ibrox.
The UoF and former Ibrox director Dave King have both been highly critical of Wallace and his fellow directors, but the board have backed the Scot to lead the club to a bright future.
A club statement said: "The absurd attacks made by individuals associated with this new scheme on chief executive Graham Wallace are disgraceful. Since Mr Wallace joined the club he has worked tirelessly to create a Rangers fit for the future.
"To question his integrity, ability or professionalism as a means to discredit him personally and to undermine the board generally is absolutely unacceptable. Mr Wallace has the board's unequivocal support."
As well as defending Wallace, the board have blasted proposals from the UoF, which are backed by King and Richard Gough, that could see fans pool season ticket cash this summer.
All money collected by Ibrox 1972 Ltd would only be given to Rangers if security is granted over Ibrox and Murray Park, but the board say the scheme "displays a twisted logic".
The statement added: "The board has no intention of granting security over Ibrox to anybody. We have already shown in our actions that our stadium is sacrosanct.
"Any supporters considering engaging with Ibrox 1972 Ltd should be clear that as the club will not grant security over Ibrox to any such organisation, there is no prospect that any commitment to this new scheme will ever come to fruition and is therefore entirely meaningless.
"Nor will the board enter into any agreement with a third party organisation on season ticket renewals, as is being suggested.
"Therefore, this scheme is a worthless academic exercise created to serve the purposes of individuals and not the greater good of Rangers."
The Union of Fans responded: "We note the latest attempt by this board to mislead and hold Rangers fans to ransom. Their latest "give us your money or the seat gets it" ultimatum is just another in a long line of misjudgements this board has made about the mood amongst the support in general."