Wolf will become the fifth person to serve in the role since the beginning of the Trump presidency.
"We have a multi-mission focus always at the Department of Homeland Security," said secretary Kevin McAleenan.
Acting DHS Secretary Kevin McAleenan pleaded for more funding at the border, but Michigan congresswoman Rashida Tlaib called it a "broken" system.
"It has become clear that the goal of this Administration is to end immigration all together," the union head said.
"The chaotic state of the Department of Homeland Security is so troubling," remarked New York Congresswoman and Appropriations Committee Chairwoman Nita Lowey to McAleenan. "It seems like the car is driving off the cliff with no one to take the wheel. Although, I guess, Mr. Secretary, you are now the driver. Congratulations."
Representative Alexandria Ocasio-Cortez criticized the former homeland security secretary for her role in the president's "zero tolerance" immigration policy, which led to family separations at the border.
Video footage of the couple engaged in sex acts with a family pet were found during a child pornography investigation.
DHS Secretary Kirstjen Nielsen and the Trump administration said, "This family chose to cross illegally."
"This is an astonishing new low in one of our nation's darkest hours. And Republicans in Congress refuse to do anything about it," said Democratic National Committee chair Tom Perez.
According to the DHS, the culprits work for a Russian hacking unit known as Energetic Bear.
As the fight to abolish U.S. Immigration and Customs Enforcement (ICE) gains ground, 19 high-profile ICE agents and leaders have signed a letter asking Homeland Security head Kirstjen Nielsen to eliminate the agency.
An ICE spokesperson told Newsweek that the operation was the largest workplace raid in the region in "at least a decade."
USCIS has already identified 2,536 naturalization cases requiring an in-depth review, with 95 being referred to the Justice Department for civil denaturalization.
A 26-year-old California man was sentenced to two years in federal prison after impersonating an ICE agent and tracking down alleged undocumented persons with fake police lights, DHS badges and bogus uniforms.
DHS officials say the National Guard's support at the border has already led to more than 1,600 apprehensions.
"We've got a leaking boat on our border," homeland security adviser Tom Bossert said.
Trump has called the U.S.-Mexico border situation a "crisis" and is sending National Guard troops to the southern border.
The snooping devices are known as 'Stingrays' and are typically purchased by law enforcement.
Out of the more than 33,000 complaints of sexual and physical abuse filed by detainees from 2010 until 2016, less than one percent of them were investigated.