The Irishman succeeded Sir Matt Busby as United manager in 1971 and took charge of 81 games with the club.
He also guided Leicester to the 1969 FA Cup final during his three-year spell in charge of the Foxes.
O'Farrell was a wing-half who played for his native Cork, West Ham, and Preston, winning nine caps for the Republic of Ireland between 1952 and 1959.
He began his managerial career at Weymouth in 1961 and spent three years at Torquay before landing the Leicester job in 1968.
O'Farrell led Leicester to Wembley the following year, where they were beaten 1-0 by Manchester City, and the Foxes were relegated from the first division three weeks later.
Leicester returned to the top flight as second division champions in 1971 and O'Farrell was quickly appointed as Busby's successor.
After a promising start which saw United top the table for the first time in three years but the Red Devils ended the season in eighth.
O'Farrell was sacked in December 1972 with United third-from-bottom of Division One.
He would later manager Cardiff, the Iran national team, and United Arab Emirates club Al-Shaab, as well having two further spells in charge of Torquay.
"It was with great sadness that the club heard the news that former manager Frank O'Farrell died on 6 March, 2022, aged 94," said the official Leicester website.
"The thoughts of everyone at Leicester City Football Club are with the family and friends of Frank at this sad time."