Amaya started the final, in which the USA claimed their second title in the tournament with a 2-0 victory over Mexico, and is expected to be in contention for the nation's Under-20 World Cup squad for the tournament in Poland this May.
The UCLA product became the first American take with the top pick since Andrew Farrell​ was taken number one overall in 2013.
Cincinnati also own the 13th pick of the first round, after acquiring it from the Philadelphia Union in a trade for allocation money earlier this week.
Haji became the second pick of the draft, with the midfielder taken by the San Jose Earthquakes.
The 19-year-old was a standout both in college and at the MLS combine.
With the third pick of the draft Orlando City went with forward Santiago Patino of Florida International University.
FC Dallas went with Canadian center back Callum Montgomery​ with the fourth overall pick. Montgomery​ played his college soccer at Charlotte.
The Colorado Rapids stayed close to home with the fifth overall pick, taking Denver University standout forward Andre Shinyashiki​.
2019 MLS SuperDraft first round
A premium was placed on attackers and pace in the early going, with four forward and two midfielders going in the top 10 picks.
The only defenders taken in the top 10 both went to the same side in FC Dallas, while just one goalkeeper went in the top 10.