Last season's Champions League semi-finalists are currently braced for a number of departures, but they continue to make their own signings ahead of the defence of their Ligue 1 title.
Netherlands international Kongolo has arrived for a reported fee of £11.41m, and he has revealed that he is excited to begin a new challenge in Monte Carlo.
The 23-year-old told the club's official website: "I am very pleased to join AS Monaco. I will discover an exciting new challenge at a prestigious and ambitious club.
"I look forward to meeting the staff, my new teammates and doing the best on the field to help the group."
Kongolo - who can play at left-back or centre-back - leaves the Dutch club having made 134 appearances in all competitions.