Born in 1936 in Matanzas, Ortega led the Catholic church in Cuba for 35 years before retiring in 2016
The cardinal who played a key role in improving ties between Cuba and the United States during the administration of Barack Obama died on Friday at the age of 82, the archbishop of Havana said.
Jaime Ortega worked as an intermediary for Pope Francis in negotiations to ease the bad blood between Washington and Havana after five decades.
Cold War rivals the US and Cuba began normalizing relations in December 2014 and the next year they restored diplomatic ties.
"Cardinal Jaime has died and while his physical absence is starting to be felt, the memories of his personal quality and tireless pastoral zeal are revived with grateful affection," said archbishop Juan de la Caridad Garcia Rodriguez in a statement.
Born in 1936 in Matanzas, Ortega led the Catholic church in Cuba for 35 years before retiring in 2016.
He submitted his resignation as Archbishop of Havana in 2011 when 75, as Vatican rules required, but his close personal friend the pope refused it then, acquiescing only in 2016.
He was the facilitator in 18 months of secret talks between Cuba and the US that led to a historical thawing of relations, since reversed by President Donald Trump.
Those talks led to a prisoner exchange and Obama's historic visit to the island nation in 2016.
Garcia paid tribute to Ortega's "friendly smile, his clairvoyant intelligence and the testimony of a successful, and often painful, priesthood."