The outcome of the votes was announced in a statement to the London Stock Exchange following a stormy annual general meeting at Ibrox.
Finance director Brian Stockbridge received 65.3 per cent backing from shareholders while his four colleagues all secured more than three-quarters of the support.
The four so-called requisitioners - Paul Murray, Malcolm Murray, Alex Wilson and Scott Murdoch - all polled close to 30 per cent of the shareholder strength.
The election - organised on a one-vote-per-share basis - came after a long-running, public and often bitter dispute between directors and the requisitioners, who had to go to the Court of Session in Edinburgh, Scotland's highest civil court, to force Rangers to include their proposed appointments in the AGM agenda.
They stated their motivation was concerns over corporate governance and the club's finances, which showed a £14.4million operating loss.
But three recent additions to the board - chairman David Somers, chief executive Graham Wallace and non-executive director Norman Crighton - appear to have convinced several influential investors to retain the status quo.
Even Stockbridge, whose unpopularity among the fans was evident at the AGM, secured his place after agreeing to pay back a £200,000 bonus in return for the support of the club's biggest shareholder, Laxey Partners, who were among the institutions to reverse their position in recent weeks.
In a statement, Somers said: "We are pleased that the board, with its focus on corporate governance, prudent financial management and strategic commercial development, has been decisively re-appointed by a high turnout of shareholders at the AGM."
Wallace, who garnered most support with a landslide 85.5 per cent vote, added: "The board sought a clear and decisive mandate from shareholders to provide a platform for stability and is pleased that the voting has provided this.
"The board recognises that improved engagement with supporters is a major area of focus and is committed to reviewing how the club engages with the wider supporter base.
"We now require a period of stability in order to take the business forward and I encourage everyone with the best interest of Rangers at heart to support fully the new board in developing the club and growing shareholder value."
Somers had earlier appealed for time to win the fans' trust and claimed they fully recognised the need to engage more fully with supporters.
As he awaited the outcome, Paul Murray insisted fans must be given a meaningful say in the running of the club.
"Whatever happens, we have brought all the issues to the fore, we have got transparency to what is happening to the club," he said.
"The important thing is that the issues won't go away, they are there for all to see.
"The most pleasing thing is that the fans have to be involved and I think the board could see that today and the board, however it is comprised, they have to embrace that.
"If they don't, then I really fear for the club."
There was one defeat for the board, who failed to secure the three-to-one majority needed to pass a special resolution to "renew the directors' authority for the disapplication of pre-emption rights".
Pre-emption rights protect shareholders from the dilution of their stakes and passing the motion would have given the board the ability to sell shares to selected investors for as little as a penny a time. The club stated that they may renew attempts to secure this privilege in future after 32.1 per cent of votes went against them.
A similar number opposed another resolution to renew the "directors' authority to allot securities", but Rangers only needed a simple majority. That allows directors to receive possible share options.
It was confirmed at the AGM that Stockbridge is contractually entitled to a potential £500,000 share option, which he has not taken up so far.
Meanwhile, Wallace insisted the club had enough money in the bank to cope with short-term demands but added: "The current operating structure we have is too high, too high even for the top division never mind the lower leagues."
The Scottish League One club raised £22million from a share issue a year go but Wallace admitted they would need to raise more funds.
"It is reasonable to assume that in order to take the club back to competing at the top levels domestically and in Europe that this will be the case," he said.
"However, this funding will only be sought once we have completed a robust business planning process that will allow us to engage with shareholders and potential investors from the platform of a well thought-out strategic plan."
The club announced the 120-day business review would include an overhaul of the club's scouting network.