The board said it accepted the resignation and "thanks him for his service to the university."
The decision followed high-level discussions by university leaders over the last couple of days. They grappled with how to treat a man who has long been identified with Temple, who wore Temple sweatshirts and hung Temple flags on the set of The Cosby Show, who for years has been a popular speaker at university commencements, and who has never faced criminal charges of assault.
Several trustees in recent days had spoken in support of the 77-year-old comedian, actor, and Temple grad, while others in the Temple community were concerned that the board leadership was staying mum and issuing no official statement.
Board chairman Patrick O'Connor spoke with Cosby on Monday afternoon and later relayed to members of the board's executive committee that Cosby had decided to step down, according to a source.
Although the university's statement did not address Cosby's appearance at commencements, multiple sources said he would not speak at graduation - which signals an era's end at the Philadelphia university.
Those pushing for Cosby's ouster were heartened by Monday's news.
"I think this is the right result, and I'm very pleased about it," said Kerry Potter McCormick, 31, a 2005 graduate and Manhattan lawyer who started the Change.org petition.
Temple undergraduate Grace Holleran was gratified by the outcome, but questioned the motive.
"I think he made the best move possible, but I feel it was probably for PR reasons," said Holleran, who wrote a piece for the Temple News this month criticizing the university for not taking action against Cosby. "I do wish Temple itself had the gall to take the initiative and dismiss him from the board, because that would have proven that the university is serious in its fight against sexual misconduct on campus."
Cosby's break with Temple is fallout from the cascade of allegations from women that, in incidents over several decades, he drugged and sexually assaulted them.
Last week, he stepped down as honorary cochair of a fund-raising campaign for the University of Massachusetts Amherst, from which he holds a master's degree and a doctorate in education. NBC canceled a proposed family-oriented Cosby sitcom, and Netflix pulled back from a Thanksgiving stand-up special.
Also Monday, Cosby offered refunds to ticket-holders who no longer wished to see him perform next weekend at the Tarrytown Music Hall in New York state, the Associated Press reported.
Maintaining ties with Cosby could have become increasingly difficult for Temple, one of dozens of colleges under scrutiny by the U.S. Department of Education for its handling of sexual-assault complaints.
O'Connor, the board chair, represented Cosby in 2005 when his fellow trustee was accused of drugging and assaulting Andrea Constand, a former Temple employee. O'Connor could not be reached for comment Monday.
The only accuser that Cosby faced in a legal proceeding was Constand, who took her case to civil court after the Montgomery County district attorney decided not to prosecute. She was working for Temple's athletic department when she met Cosby, and she told police Cosby invited her to his Cheltenham estate in 2004 to offer career advice. He gave her a pill, she alleged, and groped her while she felt too groggy to resist.
News of Cosby's departure broke on campus Monday afternoon. Raymond Smeriglio, president of Temple's student body, read the announcement at a gathering of 200 people at Temple's student government association.
"Students are happy," said Smeriglio, a senior strategic communications major from Harrisburg. "I think he did the best thing for Temple. . . .
"These allegations have become so mainstream in the media that, unfortunately, not by Mr. Cosby's choosing, our institution has now been brought down with them. We want to make sure that the reputation of Temple stays where it deserves to be."