The president said the force would be "separate but equal" to the US Air Force, adding that the move represents a "big statement".
He also promised that the United States would "return Americans to the Moon" and would eventually send people to Mars.
Mr Trump also signed a directive on the management of traffic and debris in space. This document concerns monitoring objects in orbit and sharing the information so spacecraft can avoid collisions.
"Last year the House passed a bill that would have created a space corps", says Todd Harrison, Director of the Aerospace Security Project at the Center for Strategic and International Studies (CSIS). He was joined by Mike Pence, the new Nasa administrator Jim Bridenstine and former astronaut Buzz Aldrin, the second man to walk on the moon. Will this mean hiving off the large amount of classified space activity the Air Force now handles and coordinates with the NRO?
"We must have American dominance in space", Trump said. However, critics have said the treaty has no enforcement mechanism, allowing the USA or other countries to militarize space.
With lawmakers now considering the Defense Department authorization bill, the move underscores the White House's commitment to significantly ramping up spending for various space programs, from classified high-speed missiles to more-resilient spy and communication satellites.
The National Aeronautics and Space Administration (NASA) is planning a series of lunar missions beginning next year aimed at developing the capacity for a return to the moon, said Cheryl Warner, a spokeswoman for NASA's Human Exploration Directorate.
The meeting convened to promote efforts to streamline the regulations around commercial space activities, from earth imaging to communications satellites to rocket launches.
"It is not enough to merely have an American presence in space".
Trump said he previously proposed the idea as a joke, but wanted to make it clear he was now serious about it.
Pentagon spokeswoman Dana White said that the department understands the president's guidance, and is working on the matter while taking into consideration the implications for intelligence operations for the other services.
The president said the major goal of the new program is to eventually send astronauts to Mars.