The Dakar-born forward spent three years with Brugge, with whom he won two domestic titles, having arrived in Belgium from Norwegian club Sarpsborg 08 in early 2018.
He has signed an initial deal with Monaco to keep him at the Stade Louis II until the end of the 2024-2025 season.
"I'm very happy to sign with AS Monaco and to have the opportunity to progress in a well-known and ambitious club in the French league whose history is known by everyone," Diatta told Monaco's official website upon his unveiling.
"I can't wait to discover this new environment and to work hard with my new teammates to repay this club for the confidence that they've given to me."
The 21-year-old was a member the Senegal squad that were defeated finalists at the 2019 Africa Cup of Nations where he was named Young Player of the Tournament.
He has been likened to Sadio Mane since his time with the Teranga Lions' under-20 team, with whom he excelled at the U20 Afcon in 2017, and followed that up with a run to the Round of 16 at the U20 World Cup later that year.
"We're delighted that Krepin, who was followed by many European teams, has joined Monaco," club vice-president Oleg Petrov told the club's website. "He's a talented player who has proved his many qualities in the Belgian championship and who's determined to carry on his progress with Monaco in Ligue 1.
"This demonstrates the appeal that Monaco holds, and pays witness to the efforts taken by the club to increase the team's potential over time."
Diatta makes the move to one of Europe's major leagues after some strong showings in Belgium.
The youngster has already scored nine goals and contributed two assists in 19 Jupiler League outings so far this term, starring on both wings for Brugge.
Monaco unveiled him on Thursday using the moniker the "Swiss army knife", testament both to his versatility and his diverse range of attributes.
Monaco's sporting director Paul Mitchell paid tribute to the wonderkid upon his unveiling, citing Diatta's "qualities of penetration, dynamism, finishing ability, but also his versatility, his international experience" as the reasons for his signing.
"Despite his young age, Krepin brings together numerous assets which allow him to integrate into the modern style of play employed by [Monaco head coach] Niko [Kovac]," Mitchell continued. "Krepin's arrival is part of the club's wish to raise a bit higher the group's overall level of quality for this season and to continue to build for the long term."
Monaco, who are currently fourth in the Ligue 1 table after 20 matches, host sixth-placed Marseille in the biggest match of the weekend in the French top flight on Saturday.