The former Dublin player and manager died aged 83 after a long illness.
"Kevin was a giant in every way and to his wife Mary and daughter Orla, I extend my deepest sympathy," Mr Kenny said.
The Dublin-born sporting hero, who was granted freedom of the city in 2005, made his name as a footballer at inter-county level in 1958 when he captained Dublin to All-Ireland victory when they beat Derry. The Dubs went on to win further All-Ireland glory under his management in the 1970s and 1980s.
"Heffo, as he was affectionately known by his adoring Dublin fans, was one of the real legends of the GAA," the Taoiseach said.
Mr Kenny said as a manager, Heffernan revolutionised the way the Dublin team trained.
"His All-Ireland successes brought him into the hearts and homes of Dublin and GAA fans all over the country," the Taoiseach added. "Heffo's teams rejuvenated GAA in the city and his legacy is there for all to see."
GAA president Liam O'Neill said the sportsman had an "incalculable impact" on the game, in the capital and nationally.
"The Dubs, as we know them, came into being during his era as he restored success to his native county and a pride in the team that was built on the back of the selection of Dublin-born players," Mr O'Neill said.
"He was one of the most charismatic and popular figures the association has ever produced and was at the same time an immensely modest man. I would count myself - like countless others - extremely fortunate to have met him on occasions down through the years."