The 20-year-old becomes the MLS franchise's third designated player after signing a four-year contract, his move subject to him obtaining a visa.
NYCFC coach and Arsenal legend Patrick Vieria is excited to have Medina in his ranks for the new season and expects him to have a big impact.
"We are really delighted that we have managed to bring Jesus to the football club because we believe that he's a special talent," Vieira said.
"Jesus has got talent, he's got pace, he's a really good dribbler, and he's somebody who can assist and score goals as well. For a player of such a young age, he has a really strong character and I think he will be a great addition."