The Netherlands international only signed fresh terms with the Eredivisie winners in April, but has opted to leave the club whose youth set-up he joined in 2002.
Kongolo made 23 top-flight appearances in Feyenoord's title-winning campaign and is looking forward to helping Leonardo Jardim's Monaco defend their Ligue 1 crown.
"I am very pleased to join AS Monaco," he told the club's official website. "I will discover a new and exciting challenge in a prestigious and ambitious club.
"I look forward to meeting the staff, my new team-mates and doing my best on the field to help the group."
He played for his country at the 2014 World Cup and has two caps to his name.