The chief executive and the other four members of the Gers top table won enough backing from shareholders to keep their places as Paul Murray and three fellow requisitioners fell short after a long boardroom battle.
Fans gave some board members - it also includes chairman David Somers, finance director Brian Stockbridge, James Easdale and Norman Crighton - a hostile reception.
The Light Blue legions held protests to oust the board but with all comfortably winning stakeholders' backing, Wallace is keen to end hostilities.
He said: "We should view today as a watershed moment in the history of Rangers. We have a clear and decisive vote, we have a mandate to move forward.
"What I would ask is for anyone who has got the best interests of Rangers at heart to stand behind us … to give us the opportunity to take the club back to where we all aspire to be."