The 24-year-old has penned a five-year deal with the Premier League side.
"#EFC complete signing of defender Ramiro Funes Mori for a fee of £9.5m on a five-year deal," the Toffees tweeted.
The Merseysiders also recently enlisted defender Mason Holgate from Barnsley for about £1m and 22-year-old Uruguayan striker Leandro Rodriguez from River Plate Montevideo.