Earlier on Friday, Sporting Lisbon released an official statement confirming that Silva was set for a move to the King Power Stadium.
The 28-year-old will be brought in to replace Danny Drinkwater, who completed a deadline day move to Chelsea for £35m.
Leicester requested a two-hour extension to Thursday's 11pm deadline to finalise all the necessary paperwork.
The deal remains subject to international clearance but the Foxes have confirmed the move on their official Twitter account.
#lcfc confirm terms have been agreed for the transfer of Adrien Silva, subject to international clearance https://t.co/nEKAm2EMXW pic.twitter.com/vkrm4yId7F
— Leicester City (@LCFC) September 1, 2017