He said the 5,200 soldiers will be in addition to the almost 2,100 National Guardsmen already along the border.
"Our Military is waiting for you!" he tweeted.
McAleenan said 1,900 asylum-seekers are picked up at USA border crossings a day, many of whom put themselves in the hands of violent human smugglers.
The White House is also weighing additional border security measures, including blocking those travelling in the caravan from seeking legal asylum and keeping them from entering the US.
"But we are gonna, unlike Obama and unlike others, we're going to take the people, we're going to put them in, and they're gonna wait".
U.S. President Donald Trump has hardened his stance on immigration ahead of November 6 congressional elections.
Added to the 2,000 troops already at the border, Mr Trump's announcement means the number of United States soldiers on the southern border will roughly be the same as those serving in Syria and Iraq combined.
It will also include an influx of military aviation units who will be tasked with ferrying CBP agents along the border with helicopter and airplanes, he said.
General of the USA air force on meet the press said that "to the end of the week referred to the military contingent will be placed in the South-Western sector of our border, and this is only the beginning of large-scale operations".
More than 1,000 migrants in a second caravan that forged its way across the river from Guatemala began walking through southern Mexico on Tuesday and reached the city of Tapachula - some 250 miles behind a larger group and more than 1,000 miles from the closest USA border.
The total military deployment means the number of troops at the south-western border will exceed the United States troops now in Syria and Iraq, the Wall Street Journal notes.
A second US official said there will be active duty troops along the border as part of this mission as early as Tuesday.
The figure reported Monday is a marked increase over the initial estimates of 800 troops reported last week. He would not say if terrorists were among the migrants, but told reporters that the caravan has differentiated itself from previous groups because of its level of organization. The riverbank standoff with Mexico police followed a more violent confrontation Sunday when the migrants used sticks and rocks against officers. One of the riders died from a head injury although it is unclear how he sustained it.
Susan Ormiston describes the people she's encountered in the caravan in Southern Mexico. Many are walking toward the United States with their families and say they are escaping violence and grinding poverty back home. About 600 migrants in the second group tried to cross a bridge from Guatemala to Mexico en masse Monday.
Another, smaller caravan earlier this year dwindled greatly as it passed through Mexico, with only about 200 making it to the California border.
McAleenan said those who manage to make it into the US will be apprehended and their asylum requests considered, as required by USA law.
"If they apply for asylum, we're going to hold them until such time as their trial takes place".
And the cost is "unknown at this time", he said, The Hill reported. More than 1,500 of the original group have applied for asylum in Mexico. "We want passage, that's all".