Petraeus, 60, resigned as CIA director in Nov. 2012 after it was revealed he had an extramarital affair with his biographer, Paula Broadwell. The former general will join The City University of New York starting Aug. 1 as a visiting professor for the year.
According to a person familiar with the matter, Petraeus, who received a B.S. with honors from the United States Military Academy and M.P.A. and Ph.D. degrees from Princeton University, received numerous higher offers elsewhere and will give a portion of his salary to veterans' charities.
Michael Arena, CUNY director for communications and marketing, said the funding for Petraeus' salary came from multiple private sources and not tax dollars.
"It's all fundraising that we've done," Arena said of the public university system.
Republican N.Y. assemblyman Kieran Michael Lalor wrote a letter to CUNY on Tuesday, asking the university to "reconsider" whether a public university should spend $150,000 for a "celebrity".
Martin Snyder, acting executive director of the American Association of University Professors, called the salary "outrageous" and "ridiculous" for a public university, saying $150,000 could fund two full-time university professors that could teach hundreds of students.
"What's the mission of CUNY? To teach students of New York City, not to create an exclusive discussion group with a general," Snyder said.
Snyder said many adjunct CUNY professors would get paid about $3,000 to teach one course in a semester.
Petraeus will teach one class per semester for about 15 to 20 students, said Arena.
"He'll have lots of time for interaction with students and he's teaching both semesters," Arena said, adding that he will give some public lectures. "He'll have a presence on the campus in both semesters."
According to Arena, Petraeus' class is called, "Are we on the threshold of the (North) American Decades?" and Petraeus will discuss "all areas where American innovation is leading the way" including "advanced manufacturing, life sciences, IT and energy."
Petraeus and his attorney, Robert Barnett, declined to comment to ABC News.
When Petraeus' appointment was announced by the university on April 23, he said in a statement that he was "very pleased to have an opportunity to work with the talented students at Macaulay Honors College."
"Sixty-percent of Macaulay students are the children of immigrants or immigrants themselves, and as the son of an immigrant who settled north of New York City, I identify with them and applaud their achievements in earning a place in CUNY's honors college," Petraeus said. "Beyond that, I look forward to leading a seminar at Macaulay that examines the developments that could position the United States - and our North American partners - to lead the world out of the current global economic slowdown."
The news of Petraeus' generous salary was initially revealed by the blog Gawker, which submitted a request through the Freedom of Information Act (FOIA) to CUNY. That request yielded documents that included a letter from CUNY chancellor Matthew Goldstein initially discussing a salary of $200,000.
"As I indicated, your compensation consists of a salary of $200,000 per annum, supplemented by funds (as yet to be secured) from a private gift," Goldstein writes in a letter dated March 6, 2013. "In addition, we will provide the graduate student support mentioned above to assist you with course research, administration, and grading, as well as limited travel funds for professional meetings attended as a CUNY representative."
However, Arena said that Gawker did not receive all the correspondence related to Petraeus per their FOIA request.
In later correspondence dated July 1, Macaulay Honors College dean Ann Kirschner writes to Petraeus about the $150,000 salary they settled on, saying, "Knowing that you have been sought after by other institutions, some of them offering higher salaries, I am particularly grateful that you have agreed to a lower compensation than we originally offered."
The most recent data from the American Association of University Professors in April shows full-time non-tenure-track faculty members nationwide earned a median academic year salary of $47,500 in fall 2010.
When asked whether $150,000 is typical for a high-profile visiting professor, Arena said the university system has paid a premium for such academics.
"This is an opportunity for us to get someone with vast experience both nationally and internationally to be in our classrooms with our students," Arena said. "This is a very good opportunity for our students and we want to make that available to them."
Arena added that CUNY has aggressively fundraised about $2.7 billion from private sources over the last decade.
CUNY has 23 campuses in five boroughs with a total student enrollment of about 269,000.