Talen Energy Stadium will play host to the match on July 18.
Orlando City advanced to the quarterfinal for the third time in club history and the first time since 2015. The Union are in the quarterfinals for the fifth time and the first time since 2016.
The Lions knocked D.C. United out of the competition on Wednesday at Maryland SoccerPlex, advancing on penalties after winning the shootout 4-2.
The winner of the July 18 quarterfinal will face either Chicago Fire or Louisville City in the semifinal.