The actress -- who played matriarch Katherine Chancellor on the soap opera since it began in 1973 -- had been hospitalized for an undisclosed illness since mid-April.
EW.com said the cause of her death has not been disclosed.
"My mother passed away this morning just a short time ago, peaceful with my sister by her side, in her sleep. I was going to visit this afternoon, thought I had time. Reminder to self -- time is a precious thing. I too am at peace however. I said my goodbyes several times over during the last few weeks," Bernsen wrote on Facebook.
"I'll go one last time now for a gentle kiss a final farewell for this lifetime," he said. "She has been a blaze her entire life, that beacon, that boxer I spoke of earlier. She went the full twelve rounds and by unanimous decision... won! And while her light finally gave into the wind that gives flight to all our journeys, there will always be a glimmer left behind by what she stood for. I will speak about that more in coming days, months I suppose. I will certainly dedicate what remains of my life to continue her purpose of honesty, equality, humility, empathy and love."
"Jeanne Cooper will be remembered as a daytime television legend and as a friend who will truly be missed by all of us here at the network," Nina Tassler, president of CBS Entertainment, said in a statement. "She was the longest-running cast member on daytime's No. 1 show, bringing indelible charm, class and talent to every episode. On behalf of everyone at CBS, we send our condolences to Jeanne's family, as well as the legions of fans she has amassed during her record 39 years on 'The Young and the Restless,' and throughout her career."