The clubs did not disclose the transfer fee, but British media said the deal is worth £43 million.
"I'm very, very happy to be here. It was my dream since I was young to play in the Premier League for a big team like Newcastle," Toure said in a statement.
Toure arrives after winger Anthony Gordon left Newcastle for Barcelona in a deal reportedly worth up to 80 million euros plus add-ons.
He is Newcastle's second signing after French goalkeeper Ewen Jaouen joined the club on Wednesday.
Toure, 20, made his senior debut for Ivory Coast in October last year, and made three appearances at the World Cup.
The Ivorians exited in the round of 32 after a 2-1 defeat by Norway.