In the remade versions of the classic games "Tetris" and "Snake," the player gets to build a border wall and hunt migrants as border chief Tom Homan.
In a statement to AFP, the White House says the new games aim to convey "the president's many achievements" in a way that all Americans can understand.
However, the move is drawing criticism from human rights organisations.
"It makes me sick. They've been playing with people's lives for years, and now they've made a computer game out of what they're doing," says Amerika Garcia Grewal of the Frontera Federation.
One of President Donald Trump's most prominent campaign promises was to arrest and deport undocumented migrants residing in the United States.
