The president is also expected to target so-called sanctuary cities and is reviewing proposals that would restrict the flow of refugees to the United States.
Mr Trump is expected to sign the first actions - including the measure to jump-start construction of the wall - on Wednesday during a trip to the Department of Homeland Security.
Additional actions will be rolled out over the next few days, according to one official.
Mr Trump is said to still be considering the details of plans to restrict refugees coming to the US.
The current proposal includes at least a four-month halt on all refugee admissions, as well as temporary ban on people coming from some Muslim-majority countries, according to a representative of a public policy organisation that monitors refugee issues who was briefed on the details by a government official.
Mr Trump tweeted on Tuesday night: “Big day planned on NATIONAL SECURITY tomorrow. Among many other things, we will build the wall!”
He campaigned on pledges to tighten US immigration policies, including beefing up border security and stemming the flow of refugees.
He also called for halting entry to the US from Muslim countries, but later shifted the policy to a focus on what he called “extreme vetting” for those coming from countries with terrorism ties.
While the specific of Mr Trump’s orders were unclear, both administration officials said Wednesday’s actions would focus in part on the president’s plans to build a wall along the southern border with Mexico.
He is also expected to move forward with plans to curb funding of cities that do not arrest or detain immigrants living in the US illegally, which could cost individual jurisdictions millions of dollars.
Mr Trump’s insistence that Mexico would pay for the wall was among his most popular proposals on the campaign trail, sparking enthusiastic cheers at his raucous rallies.
Mexico has repeatedly said it will not pay for any border wall.
Earlier this month Mr Trump said the building project would initially be paid for with a congressionally-approved spending bill and Mexico would eventually reimburse the US, though he has not specified how he would guarantee payments.
He will meet Mexican president Enrique Pena Nieto at the White House next week.
In claiming authority to build a wall, Mr Trump may rely on a 2006 law that authorised several hundred miles of fencing along the 2,000-mile frontier.
That bill led to the construction of about 700 miles of various kinds of fencing designed to block both vehicles and pedestrians.
The Secure Fence Act was signed by then-president George Bush and the majority of the fencing in Texas, New Mexico, Arizona and California was built before he left office.
The last remnants were completed after Barack Obama took office in 2009.
The Trump administration must also adhere to a decades-old border treaty with Mexico that limits where and how structures can be built along the border.
The 1970 treaty requires that structures cannot disrupt the flow of the rivers, which define the US-Mexican border along Texas and 24 miles in Arizona, according to The International Boundary and Water Commission, a joint US-Mexican agency that administers the treaty.
It appeared as though the refugee restrictions were still to be finalised.
The person briefed on the proposals said they included a ban on entry to the US for at least 30 days from countries including Iran, Iraq, Libya, Somalia, Sudan and Yemen, though the source warned that the details could still change.
There is also likely to be an exception in the refugee stoppage for those fleeing religious persecution if their religion is a minority in their country, which could cover Christians fleeing Muslim-majority nations.
As president, Mr Trump can use an executive order to halt refugee processing.
George Bush used that same power in the immediate aftermath of the September 11 2001 terrorist attacks.
Refugee security vetting was reviewed and the process was restarted several months later.
Other executive actions expected on Wednesday include bolstering border patrol agents and ending what Republicans have argued is a catch-and-release system at the border.
Currently, some immigrants caught crossing the border illegally are given notices to report back to immigration officials at a later date.
If Mr Trump’s actions result in those caught being immediately jailed, the administration would have to grapple with how to pay for prison space to detain everyone and what to do with children caught crossing the border with their parents.