Leicester are yet to confirm the deal, but Rijeka published a statement on their website on Wednesday to announce the switch, with the fee undisclosed.
Kramaric, who was also linked with Chelsea, is the top scorer in the Croatian top flight this season, with 21 goals from 18 appearances - nine clear of the man in second place.
His overall tally for the club stands at 55 goals from 65 appearances.
The 23-year-old has made four appearances for Croatia, scoring two goals, and made his international debut in a 2-0 friendly victory against Cyprus in September.
Kramaric's move to Leicester, who are currently bottom of the Premier League, is subject to him gaining a work permit.
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