The club's English-language Twitter account provided announced the news:
Contracts signed with Monaco for @Geo_Kondogbia. The Frenchman will undergo a medical in Italy tomorrow #FCIM pic.twitter.com/coGXbJub6t
— F.C. Internazionale (@Inter_en) June 21, 2015
Kondogbia has been in demand this summer ever since it became apparent Monaco were willing to sell.
AC Milan CEO Adriano Galliani was confident his club had a deal in place to sign Kondogbia for €40 million.
"Monaco had given us the all-clear for the sale at €40 million with payment spread over two years, €20 million and €20 million," he said in La Gazzetta dello Sport (via Football Italia).