Described by friends and colleagues as a "visionary" and a "brilliant prince," Dias is remembered as a vocal opponent of anti-Christian discrimination.
Until last year, Dias was a voting member of the College of Cardinals and played a role in selecting the last two pontiffs
-- Pope Benedict XVI and the current Pope Francis.
In a long tribute posted to Facebook, Dias' former secretary, Reuben Tellis said he had the "wonderful opportunity" to serve at the Archbishop's House for three years.
"It was during that time I was able to see the humane, gentle, spiritual and strong side of him," Tellis wrote.
"With his death, the Church has lost a brilliant and endearing prince. Leaders like him don't come by so easily. He added his own touch of specialty to the Archdiocese which will be cherished by all those who understood his vision."
1936 - 2017
Cardinal Dias was born in Mumbai on April 14, 1936
With a doctorate in canon law from Rome's Pontifical Lateran University, Dias' path towards Rome began in 1958 when he was ordained as a priest for the Archdiocese of Bombay.
On Tuesday, the Archdiocese held a memorial service at Mumbai's Cathedral of the Holy Name.
In a Facebook post, he was described as a "statesman of the Church" and a man who "served loyally, with great devotion and dedication."
In 1964, Dias joined the Holy See's diplomatic service and was posted to the Nordic Countries, Indonesia, Madagascar, La Réunion, the Comoros, Mauritius and the Secretariat of State.
Two decades later, Dias was named Archbishop of Rusubisir and Apostolic Pro-Nuncio in Ghana, Togo and Benin. He later served as Apostolic Nuncio in South Korea and Albania.
In 1996, Dias returned to India and was appointed as the Archbishop of Bombay, a post he held for 10 years.
In 2001, he was proclaimed Cardinal by former Pope John Paul II, and went on to vote in two papal conclaves. According to Rome Reports
, he said he was the first cardinal to greet the new Pope Francis.
He later moved to Rome to become the Prefect of the Congregation for the Evangelization of Peoples, the Vatican's arm responsible for missionary work.
Dias remained in the post until 2011, and retired the following year.
Ashish Selar, an MLA for the constituency of Banda, tweeted Monday: "Catholic Church loses a visionary today."
Proponent of peace
A champion of diversity, Dias spoke out against discrimination.
In 2006, a group of Indian priests was attacked by Hindu extremist groups at the inauguration of a children's hostel in the western state of Maharashtra.
"When it came to reports of attacks on Christians, he was very vociferous in his expression about how we are all called to live in peace and harmony and that people should not disrupt this," Tellis told CNN.
Tellis did acknowledge his former boss and mentor's ailing health, adding it made little impact.
"Even though he suffered ill health, he never reduced the enthusiasm with which he served. When he returned on a few occasions from Rome, he always invited his secretaries for a meal and then blessed us. During his last visit, I realized how his eyesight had deteriorated, but he recognized me by my voice."
Dias had been suffering from hypertension and diabetes, and was living in a retirement home for priests in the Italian capital. He died of natural causes.
Cardinal Dias' funeral will be held on June 21 at the Vatican Basilica in Rome, after which he will be buried in the chapel of the Palazzo di Propaganda Fide Chapel of Propaganda Fide at the Campo Verano cemetery.