By Fabrizio Romano
Both Milanese clubs have been in negotiations for the 22-year-old midfielder, with Milan originally seen as the favourites to buy him.
Rossoneri CEO Adriano Galliani, who travelled to Monte Carlo to meet with the player on Thursday, complained that Kondogbia would cost upwards of €35 million and bemoaned the player's wage demands.
Inter have capitalised on their city rivals' apprehension and are now set to complete the transfer, after he was swayed by a telephone call from Roberto Mancini on Friday.
While the two teams still have to come to a final agreement over the transfer fee, the France international has agreed a five year deal with Inter worth €4m a season plus bonuses. He is set to have a medical on Monday.
Kondogbia spent two seasons at Monaco after joining from Sevilla. The midfielder scored three goals in 33 games in all competitions in 2014-15. He was also of interest to Spanish duo Barcelona and Real Madrid, as well as a number of Premier League clubs, including Tottenham.