"We will establish a foundation for an eventual mission to Mars and perhaps someday to many worlds beyond."
The last time US astronauts visited the Moon was during the Apollo missions of the 1960s and 1970s.
On July 20, 1969, US astronaut Neil Armstrong became the first man to walk on the Moon.
Trump and Vice President Mike Pence, who heads the newly revitalised National Space Council, have previously vowed to explore the Moon again but offered few details.
Flanked by Pence and two female astronauts, Trump said the directive "will refocus the space program on human exploration and discovery," and "marks an important step in returning American astronauts to the Moon for the first time since 1972."
The goal of the new Moon missions would include "long-term exploration and use" of its surface.
A White House statement said the US "will work with other nations and private industry to return astronauts to the Moon, developing the technology and means for manned exploration of Mars and other destinations in our solar system."
Sending people to the Red Planet has been a goal of the United States for years.
The first manned Mars mission is planned for sometime in the 2030s.