It will focus on long-term explorations and use of the Moon's surface, in partnership with the private sector.
Mr Trump also said the program would lay the foundation for an eventual mission to Mars, although he did not give a date for this.
Correspondents say any realistic effort will probably need Congress to agree to a big funding boost.
There is bipartisan support for further space exploration but parties disagree over the timeline and budget.
Earlier this year, China said it was making initial preparations to send crewed missions to the Moon. During a signing ceremony, Mr Trump said: "We are the leader and we're going to stay the leader, and we're going to increase it many fold."
The new directive is recommended by the National Space Council, headed by Vice President Mike Pence.
But the Trump administration has not supplied information on how the new objective is to be achieved, and on what timescale.
With this directive, Mr Trump abandons plans set by his predecessor Barack Obama, to send humans to an asteroid near earth.
Nasa's Acting Administrator Robert Lightfoot welcomed the announcement.
"Nasa looks forward to supporting the president's directive strategically aligning our work to return humans to the moon, travel to Mars and opening the deeper solar system beyond," he said in a statement.
Photo copyright: GETTY IMAGES. Caption: Signing Space Policy Directive 1, Mr Trump said the US was "going to stay the leader".