His longtime publicist, June Rosner, said Greeley died Wednesday night at his Chicago home.
Greeley was the author of more than 50 best-selling novels, many of them international mystery thrillers, and dozens of nonfiction works. His writing was translated into 12 languages and his career spanned five decades.
The Chicago-area native wrote a weekly column that appeared in the Chicago Sun-Times and other newspapers on the relationship between religion and politics. He was a contributor to the New York Times, National Catholic Reporter and other publications.
Greeley had suffered a traumatic brain injury in November 2008, after he snagged his jacket on the door of a taxicab and fell. He spent several months in rehabilitation and underwent intensive therapy, though he never regained full cognitive function.
Greeley, who became a priest in the spring of 1965, published his final book, "Chicago Catholics and the Struggles Within Their Church," in 2010. It was a topic he had explored for years, sometimes giving him a reputation for generating controversy in the church.
"Sometimes I think that we as priests and bishops have done everything we possibly could to drive away the laity during the last 20 years," Greeley wrote in his book "Catholic Contributions: Sociology and Policy," published in 1987.
Greeley also had said neither the church nor government was willing to do much about priests who sexually abuse children.
"The sexually maladjusted priest has been able to abuse the children of the laity and thus far be reasonably secure from punishment," Greeley told a lay Catholic group in 1992.
During a news conference in 1987, Greeley said that if he were heading a church fundraising campaign, he would admit to church members that "we've really goofed. People are resentful over what they take to be the insensitivity of church leaders - particularly on matters relating to sex."
Greeley was a sociology professor at the University of Arizona and a researcher at the National Opinion Research Center at the University of Chicago. He earned post-graduate degrees from the University of Chicago in the 1960s.
The priest became often quoted and interviewed in the media. In a biography published on his website, Greeley described himself as having "unflinchingly urged his beloved church to become more responsive to evolving concerns of Catholics everywhere."
The same biography noted he was a Chicago sports fan and cheered for the Bulls, Bears and the Cubs, "while praying for them to improve."
Former President Bill Clinton listed Greeley among those who had stayed the night at the White House. Clinton's deputy White House press secretary said Greeley's novel "Irish Lace" was one of the books the then-president had on a vacation reading list in July 1997.
In 1986, Greeley offered the Archdiocese of Chicago $1 million to create a foundation to help inner-city Catholic students. The archdiocese refused the money but wouldn't say why. Greeley instead set up his own Catholic Inner-City School Fund to distribute money to the 80 Catholic schools in the city with student enrollments that are more than 50 percent black or Hispanic.