The new “Cabinet order” was signed by White House Chief of Staff John Kelly, not President Donald Trump. It allows “Department of Defense military personnel” to “perform those military protective activities that the Secretary of Defense determines are reasonably necessary” to protect border agents, including “a show or use of force (including lethal force, where necessary), crowd control, temporary detention. and cursory search.”

...

Kelly said in the signed directive that the additional authorities were necessary because “credible evidence and intelligence” have indicated that the thousands of migrants who have now made their way to the U.S. checkpoint near Tijuana, Mexico, “may prompt incidents of violence and disorder” that could threaten border officials. -Military Times

Approximately 5,900 active-duty troops were deployed to the southern US border along with 2,100 national guard to reinforce the border and bolster enforcement efforts as thousands of asylum seekers from Central America arrive in Tijuana, Mexico in the hopes of pushing into the United States. 

The Trump administration's move may raise concerns over the 1878 Posse Comitatus Act, which prohibits the use of federal military persojnnel to enforce domestic policies within the United States.  

Some of those activities, including crowd control and detention, may run into potential conflict with the 1878 Posse Comitatus Act. If crossed, the erosion of the act’s limitations could represent a fundamental shift in the way the U.S. military is used, legal experts said.

The Congressional Research Service, the non-partisan research agency for Congress, has found that “case law indicates that ‘execution of the law’ in violation of the Posse Comitatus Act occurs (a) when the Armed Forces perform tasks assigned to an organ of civil government, or (b) when the Armed Forces perform tasks assigned to them solely for purposes of civilian government.” However, the law also allows the president “to use military force to suppress insurrection or to enforce federal authority,” CRS has found. -Military Times

That said, US military forces always have the inherent right to self defense. Moreover, troops have been given a wider scope of authority in recent years to assist border agents with various actions such as drug interdictions. 

According to Military Times, defense officials say that hte language in the new directive was "carefully crafted to avoid running up against the bedrock legal limitations set in Posse Comitatus." That said, "Even [an executive order] couldn’t overcome Posse Comitatus," says Willaim Banks, author of "Soldiers on the Home Front: The Domestic Role of the American Military” and the former director of the Institute for National Security and Counter-terrorism at Syracuse University’s College of Law.

The new report appears to contradict a story from Tuesday in the Los Angeles Times that the Trump administration would begin withdrawing the troops. In fact, it appears that the pulled troops would primarily consist of engineering units which have finished their task of installing razor wire and physical obstacles at border crossing points - while the original scope of the mission had authorized a deployment until December 15, unless the Department of Homeland Security requested an extension.