In recent years, where stadium naming rights could be sold, universities and professional sports teams have sold them — to airlines and banks and companies that sell beer, soda, doughnuts, cars, telecommunications, razors and baseball bats. This led to memorable examples like Enron Field, the KFC Yum! Center and the University of Phoenix Stadium.

On Tuesday, that trend took another strange turn when Florida Atlantic University, in Boca Raton, firmed a deal to rename its football building GEO Group Stadium. Perhaps that pushed stadium naming to its zenith, if only because the GEO Group is a private prison corporation.

For this partnership, there is no obvious precedent.

The university’s president described the deal as “wonderful” and the company as “well run” and by a notable alumnus. But it also left some unsettled, including those who study the business of sports and track the privatization of the prison industry. To those critics, this was a jarring case of the lengths colleges and teams will go to produce revenue, of the way that everything seems to be for sale now in sports — and to anyone with enough cash.

“This is an example of great donor intent, terrible execution,” said Paul Swangard, the managing director at the University of Oregon Warsaw Sports Marketing Center. “Here’s a guy with strong ties to the university, who wants to make a difference, and is mixing his philanthropic interest with a marketing strategy that doesn’t make any sense.”

The GEO Group, which is based in Boca Raton, secured the naming rights with a $6 million gift, paid out over 12 years through its charitable arm, the largest such donation in Florida Atlantic’s athletic history. In a news release, the university said the money would finance athletic operations, the stadium, scholarships and “academic priorities.”

The stadium, which opened in the fall of 2011, cost $70 million and seats more than 29,000. It offers 6,000 premium seats, 24 suites and 26 loge boxes.

In a telephone interview, the university’s president, Mary Jane Saunders, noted that GEO’s chairman, George Zoley, had two degrees from Florida Atlantic and once served as chairman of the Board of Trustees. Four members of the board, Saunders added, have also worked for the GEO Group, including two past student government presidents. The company’s corporate headquarters overlook the stadium.

Saunders said the GEO Group emerged as the “strongest prospect” for a naming rights partner, and at an important time, as Florida Atlantic moves from the Sun Belt Conference into Conference USA next season.

“We use no state money to run our athletic program,” she said. “It’s important for us to use our naming rights to fund the stadium and fund scholarships.”

Critics say the cost may be too high. One is Bob Libal, the executive director of Grassroots Leadership, a social justice group that opposes private prison systems.

Libal said the GEO Group “poured enormous resources” in recent years into “attempting to take over a large portion of the Florida prison system.” He said the company’s usual practices included lobbying and charitable donations, often in areas where it operated facilities or planned to. To that end, this move could represent a way for the company to rebrand itself in Florida, he added.

“It’s startling to see a stadium will be named after them,” Libal said. “It’s like calling something Blackwater Stadium. This is a company whose record is marred by human rights abuses, by lawsuits, by unnecessary deaths of people in their custody and a whole series of incidents that really draw into question their ability to successfully manage a prison facility.”

GEO Group reported revenues in excess of $1.6 billion in 2011, income generated mostly from state and federal prisons and detention centers for illegal immigrants. The company owns or runs more than 100 properties that operate more than 73,000 beds in sites across the world. It holds nearly $3 billion in assets.

The company has been opposed by civil liberty and human rights groups and immigrant rights organizations. It has been cited by state and federal regulators and lost a series of high-profile lawsuits.

The company declined to make anyone available for interviews. It asked for a list of questions to be e-mailed and responded mostly with information contained in the initial news release about the stadium naming. An e-mail from a spokesman read, in part, “We have always adhered to the highest standards in our industry and have shown a commitment to philanthropy and good corporate citizenship, and we believe this very important gift, which will help thousands of students over the next twelve years, is representative of that commitment.”

Asked if Florida Atlantic had looked into the allegations against the GEO Group, Saunders said, “We think it’s a wonderful company, and we’re very proud to partner with them.”

An N.C.A.A. spokeswoman said individual universities made decisions regarding naming rights, with no N.C.A.A. involvement.

Swangard, at the University of Oregon, said he told his students that “sponsorship begins and ends with objectives” and “sponsorship is not philanthropy.” He said universities should draw the line where they can defend the natural association that comes with the company they do business with.

“It can’t just be about the money,” he said. “That’s great, but at what cost? Now, across the country, they’re going to say that Florida Atlantic can change its uniforms to stripes. That’s not fair. But that’s reality.”

As are the financial requirements of big-time college sports. To that end, said David Ridpath, a professor of sports administration at Ohio University and a member of the Drake Group, a network of professors who lobby for academic integrity in college sports, those constraints must also be considered.

In an e-mail, he described his response to the naming rights deal as “ambivalent,” adding: “The short answer is, I understand to an extent. But it does appear we’re prostituting ourselves to the highest bidder regardless of what they represent. Again — the sanctity of higher education matters little when the dollars are needed.”