The Principality club spent last season in Ligue 2, and although they failed in their attempt to regain their top-flight status at the first attempt, they have recently secured big-money backing from Dmitry Rybolovlev.
And they have wasted no time in spending a sizeable fee on the 18-year-old, who has won eight caps for Argentina at Under-17 level.
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"Monaco are delighted and proud to announce the formalisation of the transfer of Lucas Ocampos from River Plate," a statement on the club's official website read.
"The young 18-year-old Argentine has signed a six-year contract with the club, and will be presented to the media on August 17."
Ocampos himself stated that he was looking forward to helping his new club seal a return to top-flight football as soon as possible.
"I want to win Ligue 2 and play in Ligue 1," he told RMC. "I also want to play in the Champions League with Monaco.
"Everything is very beautiful here. Right now, all I hope to do is play, and above all, win."
Monaco got their Ligue 2 campaign off to the perfect start with a 4-0 win over Tours on July 30, but could only manage a 0-0 draw with Stade Lavallois a week later. Friday's win over Istres leaves them in second place.
Andrea Raggi, Jakob Poulsen, Delvin Ndinga and Emir Bajrami have also moved to Stade Louis II this summer, while Claudio Ranieri has joined as coach.