Moores was a lifelong Reds fan and served as chairman for 16 years from 1991.
His family founded the Littlewoods retail empire, and his uncle Sir John was twice Everton chairman in the 1960s and 1970s.
Moores' wife of 39 years Marge died just a few weeks ago.
The Moores family held a majority stake in Liverpool for more than half a century and, after taking over, he and chief executive Rick Parry oversaw the appointments of Roy Evans, Gerard Houllier and Rafael Benitez.
The club won 10 major honours during his tenure including the Champions League in 2005.
However, in the pursuit of external investment to help develop a new ground Moores sold his controlling interest to Tom Hicks and George Gillett two years later.
"The thoughts of everyone at Liverpool FC are with David's family and friends at this difficult time," said a statement from the club.
Iconic former player and manager Kenny Dalglish wrote on Twitter: "Marina and I are both very saddened by the passing of David Moores.
"He was a loyal Liverpool fan whose dream came true when he was appointed chairman, and he did a tremendous amount to help the club.
"Our condolences go to his family. He'll be greatly missed by all who knew him. RIP."
Jamie Carragher also paid tribute on Twitter: "RIP Mr Chairman. When I think of the good times I had at [Liverpool] David Moores was at the heart of it.
"He will be sorely missed. Thank you for what you did for me & the club."