The 23-year-old, who has scored twice in just four appearances for his country, has been granted a work permit and could go straight into the squad for Saturday’s clash with Stoke.
Manager Nigel Pearson told the club’s official website: “We’ve watched Andrej for a long time so we knew were signing a player that could add great quality to English football and I’m delighted that the relevant authorities have seen the situation the same way.
“He’s an extremely talented young footballer and I’m delighted we have been able to finalise his signing. He is potentially a very important addition for us.”
Kramaric scored 28 goals in 31 games for Rijeka this season and becomes Leicester’s second signing of the January transfer window following the arrival of goalkeeper Mark Schwarzer from Chelsea.