The 20-year-old joined Lyon's youth ranks in 2008 and spent three campaigns with the B team before stepping up last season.
Monaco vice-president and chief executive Vadim Vasilyev said: "We are pleased to announce the signing of Jordy Gaspar to AS Monaco.
"He is a young French prospect recognised for his potential and who will find all the conditions to progress here under the orders of Leonardo Jardim."
Since winning the title, Monaco have sold Bernardo Silva to Manchester City and seem likely to lose teenage sensation Kylian Mbappe.
However, they have added Youri Tielemans to their ranks and tied Radamel Falcao and Jardim down to contract extensions.