LAFC selected Joao Moutinho from Akron with the first pick of the MLS SuperDraft on Friday.
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Villa, who was recalled for the first time in three years in August, was omitted from the squad a month later because of an injury.
New York City FC signed winger Ismael Tajouri from Austria Vienna on Friday.
New York City FC completed the singing of Benin international center-back Cedric Hountondji on Thursday.
Medina comes in to take the designated player place available following the retirement of Andrea Pirlo.
Sporting Kansas City acquired forward Khiry Shelton from New York City FC in a trade for right-back Saad Abdul-Salaam on Thursday.
New York City FC boss Patrick Vieira has spoken of his desire to coach in Italy after visiting Serie A club Napoli.
In exchange for the 32-year-old, D.C. gave up $75,000 General Allocation Money and a 2018 International Roster Spot.
Every legend has his day, they say (we think). And Dec. 6, 2017 will be forever known as Andrea Pirlo's in New York City.
Patrick Vieira insists he is "not chasing a job in Europe," with the highly rated New York City FC boss happy with at the MLS franchise.
David Villa has played down talk of a return to European football and said he is focused on postponing retirement as long as possible.
Kaka and Andrea Pirlo are two of the finest players of their generation, but MLS stays were forgettable. What can the league learn from their tenures?
Andrea Pirlo walks away from the game having built so much. James Horncastle looks back on his career.
David Villa was nothing short of magnificent for New York City FC this season, but the goal-scoring burden proved to be too much for the club captain.
Andrea Pirlo is the kind of aging superstar signing that MLS is veering away from, and his retirement represents the close of a chapter in the league.
Italy legend Andrea Pirlo has thanked New York City FC and its fans after retiring as a player.
Columbus Crew SC fell 2-0 to New York City FC on Sunday, but the Crew move on to the Eastern Conference final through a 4-3 aggregate win.
The Columbus Crew came out on top against New York City FC 4-3 on aggregate despite losing the second leg 2-0 at Yankee Stadium on Sunday.
The Columbus Crew held on to eliminate second-seed New York City FC in the Eastern Conference, will face Toronto in conference finals.