The 20-year-old, who reportedly agreed personal terms with West Ham during the summer transfer window, has agreed a deal that will keep him at Villa Park until 2030.
Duran has scored six times this season including the only goal in last week's 1-0 win against Bayern Munich in the Champions League, despite starting just once in all competitions.
The Colombia international joined Villa in January 2023 from MLS side Chicago Fire, scoring five goals in 23 Premier League appearances last season, most as a substitute.
Following last week's win against Bayern, Villa boss Unai Emery said the player's potential was "huge".
"Sometimes he has been impatient and I need to speak to him as a person and connect to him as a person," he said.
"As well as a player to try to let him play, putting him on the field because his talent is there and the capacity to help us."
Villa are fifth in the Premier League table after seven games, four points behind leaders Liverpool.
