A towering centre-half, Yeats represented Liverpool for 10 years between 1961 and 1971, playing a major role in their rise from a second-division side to an all-conquering English team.
Yeats made 454 appearances for the Merseyside outfit across all competitions, scoring 16 goals and winning six major honours, captaining Liverpool to their first-ever FA Cup triumph in the 1964-65 season.
The Scotsman also lifted the 1963-64 and 1965-66 First Division titles with Liverpool, as well as three consecutive Charity Shields from 1964 to 1966.
From those 454 matches in a Liverpool jersey, Yeats wore the captain's armband in over 400 of them, and only Steven Gerrard has captained the Reds' men's team on more occasions than the late Scotsman.
"Liverpool FC is mourning the passing of legendary former captain Ron Yeats," Liverpool said in a statement. "In the words of Bill Shankly, a 'colossus' in club history, the Scot died on Friday night at the age of 86, having sadly suffered with Alzheimer's in recent years.
"The thoughts of everyone at LFC are with Ron's wife, Ann, all of his family and his friends at this incredibly sad time. Flags across club sites will be lowered to half-mast today as a mark of respect."
'Yeats was the rock of Liverpool's resurrection'
Yeats began his career at Dundee United before moving to Liverpool, and the defender also represented Tranmere Rovers, Stalybridge, Barrow, Los Angeles Skyhawks, Formby and Rhyl after leaving Anfield.
The two-time First Division winner only won two caps for the Scotland national team, though, starting in a friendly loss to Wales in 1964 before making his second and final appearance for his nation in a 3-0 defeat to Italy one year later.
After hanging up his boots, Yeats spent 20 years as Liverpool's chief scout from 1986 to 2006, during which he unearthed another revered Liverpool centre-back in Sami Hyypia.
Sports Mole editor Barney Corkhill:
"It is difficult to overstate the importance of Ron Yeats in the history of Liverpool.
"The club has boasted many other legendary centre-backs since his arrival in 1961 - from Tommy Smith and Alan Hansen to Jamie Carragher and Virgil van Dijk - to the extent that Yeats may struggle to get into an all-time XI, but he was one of the cornerstones around which Bill Shankly was able to build Liverpool into the dominant force in English football.
"Liverpool were a Second Division side when he arrived, but by the time he left a decade later he had captained the team to two top-flight titles and the club's first-ever FA Cup.
"Shankly himself hailed Yeats's signing as the "turning point", and while Ian St John, Ian Callaghan, Roger Hunt et al stole most of the headlines throughout the Reds' resurrection, Yeats was the rock on which it was all built.
"Nicknamed 'The Colossus' for good reason, Yeats also played a unique role in Liverpool's switch to their now-iconic all-red kit - one of a number of his contributions to the club, without which Liverpool FC may not be quite the worldwide institution they are today."