The new military service, the first in more than 70 years, falls under the US Air Force.
At an army base near Washington, Mr Trump described space as "the world's newest war-fighting domain".
"Amid grave threats to our national security, American superiority in space is absolutely vital," he said.
"We're leading, but we're not leading by enough, but very shortly we'll be leading by a lot."
"The Space Force will help us deter aggression and control the ultimate high ground," he added.
The funding allocation was confirmed on Friday when the president signed the $738bn (£567bn) annual US military budget.
The launch of the Space Force will be funded by an initial $40m for its first year.