Under Space Policy Directive 1, the moon is seen as a stepping stone toward the ultimate goal of Mars exploration.
The better known Buzz Aldrin, the second man on the Moon after Armstrong and a fervent advocate of future space missions, was also present at the ceremony but not mentioned by Trump during his speech.
Harrison Schmitt, an astronaut on Apollo 17, stood by the president while he signed Space Policy Directive 1. "This time we will not only plan on flag and leave our footprint".
The event will coincide with the 45th anniversary of the last crewed mission to land on the moon. "It marks an important step in returning American astronauts to the moon for the first time since 1972, for long-term exploration and use".
In approving the new policy, Mr Trump abandoned what had been a goal of his predecessor, Barack Obama, who in 2010 backed a plan to send humans to a near-Earth asteroid.
NASA says work toward the new directive will be reflected in NASA's 2019 budget. Statements from administration officials, including Vice President Mike Pence, has have made clear their interest in human lunar missions.
The Commercial Spaceflight Federation - a member organization for human spaceflight companies - released this statement from its president, Eric Stallmer: "CSF applauds President Trump for signing Space Policy Directive 1, which directs NASA to partner with the US commercial space industry to return Americans to the Moon".
Astrobotic, a Pittsburgh-based startup that spun out of Carnegie Mellon University, praised Trump's announcement, urging Nasa to rend robotic landers to the moon starting in 2020 in advance of a human return.
On July 20, 1969, United States astronaut Neil Armstrong became the first man to walk on the Moon.
Under the directive, the US Government is also expected to work closely with other nations and private industry. As did industry groups the Coalition for Deep Space Exploration and the Commercial Spaceflight Federation, whose president Eric Stallmer said that commercial companies have "invested hundreds of millions of dollars in private capital to develop innovative capabilities for lunar transport, operations and resource utilization".