Andrews played an instrumental part in the club climb into League One.
The club announced his passing before Saturday’s National League fixture with Sutton United.
“It is with great sadness that we have to report that Club President and former Chairman Dave Andrews passed away during the evening of Friday 2nd November after a short illness, aged 79,” a statement read.
“Our thoughts this morning are with his family, wife Pat and children Paul, Kay and Geoff.”
Under Andrews the club had their greatest even hour, defeating Rotherham United to earn promotion into the third tier for the first time ever back in 2010.
The manager who helped take them there, now Barnet boss John Still, said he was “deeply saddened” by the news.
Funeral details have yet to be confirmed.