The Colombia international moves to the Saudi Pro League club for a fee rising to €80m.
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Duran's contract with Al-Nassr runs to 2030.
"Aston Villa can confirm that Jhon Duran has joined Al Nassr," the club said.
"Everyone at Aston Villa would like to wish Jhon all the best in the next step of his professional career."
Duran has scored 12 goals in 29 games for Villa this season.