The University of Phoenix, one of the nation’s largest for-profit college chains, agreed to a $191 million settlement on Tuesday with the Federal Trade Commission, which said the school had lured in students with fraudulent claims about partnerships with major companies that one of the chain’s own executives had described as “smoke and mirrors.”

The school’s deceptions centered on a marketing campaign that invoked A-list companies like Microsoft and Twitter, which affected students who enrolled between October 2012 and December 2016.

The University of Phoenix did not admit wrongdoing under the settlement. It will pay a $50 million penalty to the F.T.C. and cancel $141 million in debts, largely for unpaid tuition and fees, owed by former students who first registered during that four-year period. Tens of thousands of students will be covered, most likely for relatively modest sums.

The F.T.C. filed a complaint in federal court in Arizona on Tuesday that described the advertising campaign. Starting in 2012, a series of television ads and online postings from the university heralded its “corporate partnerships” with more than 2,000 employers, including the American Red Cross, AT&T and Yahoo. The ads said the school worked with those employers to “shape our curriculum” and “create options” for its graduates.