McGuire spoke to board members about stepping down after he was cited by the AFL for breaching its racial vilification policy over his "King Kong" reference to the Swans star.
However the board issued a statement on Thursday giving McGuire its full support.
Vice-president Jack Kennedy described McGuire as "a magnificent president" and said his ongoing leadership was "essential".
"While we accept that Eddie made a mistake that caused serious offence to Adam Goodes and many more, we balance this against the work Eddie and the board have done, and continue to do, to make Collingwood an institution in football and society that our entire family can be proud of," Kennedy said.
"Eddie has led with distinction for almost 15 years and a hallmark of his time has been a commitment to positive change on and off the field, at Collingwood and beyond."
Collingwood coach Nathan Buckley also came out strongly in support of McGuire on Thursday.
"He (McGuire) is as you imagine quite distraught and disappointed with his comment and how that's been perceived and the damage that it's caused," Buckley said.
"We support him. It was just a bad moment, a poor comment, and Eddie has said all of those things and apologised unreservedly."
Buckley said McGuire should be given credit for his three decades of involvement in broadcasting.
"He's made a blue and it's there for all to see and he's been apologetic for it," Buckley said.
Buckley said McGuire was all for equality and had led the Magpies brilliantly.
"He had no intent to hurt or to harm. He definitely had no intent to incite hatred, which is the true term for vilification.
"The person who is being hated at the moment is actually Eddie, for his comments, and he accepts that.
"But as you can imagine it's a tough time for him. It's a tough time for Adam Goodes.
"It's a tough time for Aussies in general because the very fabric of who we are and the way that we go about things, the casual racism as [Collingwood player] Harry [O'Brien] put it, the casual discrimination, not just of colour but religion, ethnic background, sexual preference.
"Anything that's different, we want to pick at it as Aussies. Potentially this is a wake-up call for everyone."
