The Dutchman had been on loan at Bundesliga side Hoffenheim, where he was recalled ahead of the transfer deadline.
Locadia joined the Seagulls from PSV Eindhoven during January 2018 in a reported £14million deal and has scored six goals in 43 games for the club.
The 26-year-old, who has made two Premier League appearances for Brighton this season, is set to join up with Cincinnati when the transfer window opens again in America on February 12.
Cincinnati will have the option to make the deal permanent at the end of the upcoming MLS campaign, which starts on March 1.
Locadia said on the Cincinnati website: "I am looking forward to a new opportunity.
"I want to try to help the team build new memories and be an important player for the team."
Cincinnati general manager Gerard Nijkamp said: "We are excited to bring in a proven forward in Jurgen to strengthen our attacking abilities.
"He is a talented goalscorer in his prime and we feel adding an impact player of his calibre will be a great addition to our club."