The United States Space Force was mentioned in a public speech on March 13th of 2018. 
"Space is a war-fighting domain just like the air, land, and the sea. We may even have a Space Force... because we're doing a tremendous amount of work in outer space" 
Trump also announced that 'very soon we'll be going to Mars'. 
On Monday, June 18th of 2018, Donald Trump instructed the US Pentagon and Department of Defense to begin the formation of the Space Force. He made the announcement at a White House conference. 
General Dunford would be leading the formation of the new agency. In his closing remarks, Trump said "There's No Place Like Space... Good Luck". He also spoke about the importance of Privatization of space travel, citing a vast number of wealthy Entrepreneurs who wish to travel outside of Earth. Though apprehensive towards new Regulations, Trump acknowledged the need for them in the interest of National Security.