One person familiar with his decision said the secretary wanted to be closer to his family in Rhode Island, where he held a state post before joining Corbett's administration in 2011.
It was not immediately clear who might replace Alexander. A name mentioned is Beverly Mackereth, a former York County legislator who now heads DPW's office of children, youth and family.
Alexander frequently has been a lightning rod for criticism of the administration's cuts to social welfare services - particularly in his efforts to carry out a mandate to cut "waste, fraud, and abuse" in the department.
In January 2012, Alexander announced the department was instituting an asset test, making the amount of food stamps people can receive contingent on the assets they possess.
The move bucked national trends, favored by both Democrats and Republicans, to eliminate such tests because of what critics called the punitive impact on elderly people saving for their burials, poor people trying to save enough to escape poverty, and working- and middle-class people who lost their jobs in the recession and would have to liquidate assets to feed their families.
Alexander's department also faced questions about children being dropped from Pennsylvania's Medicaid rolls. Between August 2011 and January of last year, about 130,000 people, including 89,000 children, were dropped from the federal health insurance system for the poor - a number so high that the Obama administration stepped in, seeking detailed information to determine whether anyone had been wrongly struck from the rolls.
Alexander also occasionally raised eyebrows in the Capitol for matters having little to do with welfare policy - such as memos he issued early in his tenure outlining a dress code for executive-level staff. For women, that included a ban on open-toed shoes and a requirement of nylon stockings or tights - even in summer - irking some female employees.
Last year, one of Alexander's top appointees in the department had to quit after The Inquirer revealed that the aide was moonlighting as editor of a conservative journal. In that role, the aide had opined on such matters as studies purporting to show the benefits to women of forgoing contraception, and enumerating the benefits of having mothers stay out of the workforce.
Last December, Alexander faced questions again when a Harrisburg online news service, PA Independent, reported that he had been driving a state-owned car from Harrisburg to his home in Rhode Island dozens of times a year.
Asked about it at the time, Alexander told The Inquirer: "My family lives in Rhode Island, I have two small children and a wife I love very much. I also pay for part of that vehicle. It comes out of my check, and I've been allowed to use it to go back and forth."
Reacting Monday to word of Alexander's imminent exit, Sharon Ward, director of the Pennsylvania Budget and Policy Center, a left-leaning think tank, said, "He presided over a number of changes that have really been a setback for the very poorest Pennsylvanians." She pointed to children being removed from Medicaid rolls and many adults losing General Assistance benefits.
Carol Goertzel, chief executive of Pathways PA, a nonprofit in Holmes, Delaware County, that aids women and children, said, "I just hope the next secretary of public welfare will be somebody who's really looking at the welfare of the public."
Alexander would be the second cabinet official to leave the Corbett administration. Last October, Health Secretary Eli N. Avila quit his $146,000-a-year post after less than two years in the job.
Avila, too, had become a frequent topic of conversation in Harrisburg, but for different reasons. He made headlines for an angry dispute with a diner owner over the freshness of an egg sandwich. The owner later sued, alleging that Avila retaliated for the episode by trying to block him from landing a state contract. Avila said he was just trying to protect public health.
The suit is pending.
Contact Angela Couloumbis at 717-787-5934 or firstname.lastname@example.org, or follow on Twitter @AngelasInk.
Inquirer staff writer Alfred Lubrano contributed to this article.