Born Rita Rizzo to a poor family in Ohio, she became known to millions of viewers of her show as Mother Angelica.
Her health had been declining since she suffered a stroke in 2001.
Alabama Governor Robert Bentley was among those to pay tribute.
"She left an indelible mark on Alabama, the Catholic Church and the world as a whole,`` he said.
EWTN`s chairman Michael Warsaw said Mother Angelica would always personify the network.
"In the face of sickness and long-suffering trials, Mother`s example of joy and prayerful perseverance exemplified the Franciscan spirit she held so dear," he said.
Mother Angelica became a nun in Cleveland aged 21 and founded a new monastery near Birmingham in Alabama in 1962.
She launched EWTN after refusing to continue broadcasting from a secular TV station that she said was also broadcasting blasphemous films, the Catholic News Agency reported.
Although ill health prevented her from appearing on her "Mother Angelica Live" show towards the end of her life, old episodes continued to be broadcast.
EWTN claims to be the world`s biggest religious media network. It has 11 channels reaching more than 250m homes in 145 countries. It also operates radio stations and newspapers.
The network, which has been at times been criticised by both liberal and conservative Catholics, says it tries to be loyal to the Vatican and reports extensively on the Pope`s statements and trips.
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