Kondogbia, 20, agreed a five-year deal with Claudio Ranieri's men on Friday after a week of speculation linking him with a move to Stade Louis II.
Sevilla released a statement on Tuesday stating that Kondogbia "was history at the club", with reports tipping Monaco to buy out his €20 million (£17.1m) release clause.
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The former Lens man had been linked with a number of top European clubs including Real Madrid, Juventus and Arsenal last season and in the summer, but the Ligue 1 side have won the race for the youngster's signature.
Kondogbia made 40 appearances last year for Sevilla, scoring one goal.